StudentID: 1
Nickname: test
Q3: C
Honorcode: 2
Date: 2/23/00
Time: 12:00:25 PM
test1
test2
StudentID: 101186427
Nickname: spunk
Q3: D
Honorcode: 1
Date: 2/23/00
Time: 12:38:26 PM
r squared is the porportion of variance explained or accounted for. This name is used because SSt is a kind of measure of variance from the dependent variable's mean and is closely related to the variance of the dependent variable. (SSt is the same as SS in the variance formula- the number that when divided by N gives the usual variance.) Proportionate reduction in error is how much of SSt is reduced, or accoutned for, by the prediciton model. Thus, proportionate reduction error is also the proportion of a kind of variance that is reduced. Squaring r or using (SSt-SSe)/SSt both calculate the percent of variance that is accounted for. The main difference between the two is that r squared is easier to compute.
To find this answer one must first find the value of the slope(b) and the value of the y-intercept which is (a). To find the slope you need to use this formula:b=B(SDy/SDx). After you put in the appropriate numbers -.90(.14/.22)= -.57 you will find that the slope is negative -.57. Now you have to find the value of a. You do that by using the formula a=My-b(Mx). After you put the appropriate numbers into the equation you will find that a equals 1.02. .75--.57(.48)=1.02. Now that you have calcuated both the slope and the y-intercept you have found the raw-score prediction equation. The predicticted y= 1.02-.57(x). To find the proportion of housework a woman would make if she contributes a proportion of .90 of the household income is simple to calculate. you simply put .90 into the formula: y=1.02-.57(.90). When you calculate this you will get .507 as your perdiction.
StudentID: 101736154
Nickname: mercury
Q3: D
Honorcode: 1
Date: 2/23/00
Time: 1:51:55 PM
SST is thethe sum of squared differences (squared errors) of each score from the predicted score when predicting from the mean. It is sometimes also called the variance. SSE is the sum of the squared differences (squared errors) between each score and its predicted score. Using these two numbers one can find the extent to which one make less error using the prediction model than using the mean. This comparison indicates ones accuracy of the prediction model and is called the proportionate reduction in error. First one finds the reduction in error, by finding the difference between square error when predicting from the mean (SST) and the squared error usin gthe prediction model (SSE). This number represents the amount of squared error reduced by using the prediction model. This number is then divided by the total amount that it could be reduced (SST). Using the mean is not a very precise method because it produces a lot of error. Therefore, this equation allows one to see how much better one could do. It is the proportion of the squared error one would make using the mean is reduced by using the prediction rule.
b= B(SDy/SDx)= -.90(.14/.22)= -.58; a=My-B(Mx)= .75- -.90(.48)= .75- -.432= 1.18; Y^= a + bx = 1.18 - .58x. Prediction of what proportion of the housework women would make= Y^= 1.18 - .58x = 1.18 - .58(.90) = .66
StudentID: 101968018
Nickname: nicholas
Q3: D
Honorcode: 1
Date: 2/23/00
Time: 5:53:03 PM
R^2 is the percent of variance or error explained, meaning it is a percentage of the variability that the independent variable can be explained by the dependent variable. So, in the formula, you are subtracting all the deviations from the Y and the Mean value which is the amount of squared error when predicting without a model, summing them, and subtracting the error between expected Y and Y values which are from the prediction model, then dividing them by the difference in Y and mean values. This comparison is an indicator of the accuracy of the prediction model. So now you are seeing how much better you can do with your prediction model in comparison to using the mean, in terms of a proportionate reduction in error.
Y = 1.025 + (-.5727)X is the raw-score prediction equation. Given a proportion of .90 of the household income contributed would give a raw-score of .5096.
StudentID: 101780234
Nickname: lucky
Q3: D
Honorcode: 1
Date: 2/23/00
Time: 8:35:10 PM
The sum of squared error, or SSError, is the sum of the squared error when using a prediction model; the sum of squared products of all the actual scores minus their predicted scores. The total sum of squared error, or SSTotal, is the sum of squared error when predicting using the mean; the sum of the squared products of all the actual scores minus the mean. With a good prediction, the SSError should be less then the SSTotal. This comparison is an indicator of the accuracy of our prediction model and is called the proportionate reduction in error, (r^2). First we compute SSTotal - SSError, which is the amount of squared error reduced by using the prediction model. Then, this value is divided by the total amount that could be reduced (SSTotal), giving the proportionate reduction in error. This proportion is the percent of variance that is explained by the predictor variable. The higher the proportion, the higher the percent, and the higher the correlation. In other words, a greater portion of the data is explained by the predictor variable.
(a= My - bMx) a= .75 - (-.573(.48))= 1.025 (b= B (SDy/SDx) ) b= -.90 (.14/.22)= -.573 (Y= a + b(x)) 1.025 + -.573(.90)= .51
StudentID: 101954741
Nickname: angelfire
Q3: D
Honorcode: 1
Date: 2/23/00
Time: 8:42:25 PM
To compute the proportionate reduction in error, you first find the reduction in error, the difference between the squared error predicting from the means (SStotal) and the squared error using the prediction model (SSerror). That is, you compute SStotal-SSerror. Then this number, the amount of squared error reduced by using the prediction model, is divided by the total amount that could be reduced (SStotal). The proportionate reduction in error always equals the correlation coefficient squared. The proportionate reduction in error is also sometimes referred to as the proportion of variance accounted for. This can be explained because the SStotal, or total squared error when predicting from the mean, is a kind of measure of variance of the dependent variable. (When divided by n (number of scores), the SStotal gives the usual variance). Proportionate reduction in error is how much of SStotal is reduced, or accounted for, by the prediction model. Thus, we subtract SSerror, the sum of the squared errors, and divide by SStotal.
To generate the raw score prediction equation, one must first find the value of (a) and the value of (b). The formula for a=My-b(Mx) and the formula for b=(beta)(SDy/SDx). Plug in the numbers given in the problem to each formula, and then use those numbers to create the raw-score prediction equation, y(cap)=(a)+(b)(x), which in this particular problem is y(cap)=1.025-.573(x). To make a prediction of what proportion of the housework a woman would make if she contributes a proportion of .90 of the household income, one should place .90 as (x) into the raw score prediction equation: y(cap)=1.025-.573(.90), which equals .51.
StudentID: 100962404
Nickname: Sunny
Q3: D
Honorcode: 1
Date: 2/23/00
Time: 8:46:33 PM
The proportionate reduction in error is also known as the proportion of variance accounted for. By subtracting the sum of squares of the errors from the total sum of squares, you are left with the sum of squares which are explained, or accounted for. Dividing this number by the total sum of squares gives you the proportion accounted for.
b = -0.9(.14/.22), b = -.573 a = .75 - (-.537)(.48), a = 1.03 Y(predicted)=1.03 - .573X Predicted Y when X=0.90 is 0.5143
StudentID: 101194842
Nickname: moggy
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 1:11:09 AM
The reason that the formula would be equal to the proportioate reduction on error is because you first take the squared error predicting from the mean and subtract the squared error using the prediction model. This is the amount of squared error reduced by using the prediction model. Then you take that amount and divide it by the total amount that could be reduced. Using just the mean for this is no good because it produces a lot of error, so the proportionate reduction of error reduces that number.
Part 1: b=-.57 and a=1.02(where it crosses the y-axis), so Y=1.02+(-.57)X Part 2: She would contribute .74 of the housework.
StudentID: 100734537
Nickname: cheesecake
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 10:33:11 AM
The proportionate reduction in error (r^2) indicates the accuracy of the prediction model by showing how much of the total error possible (SSt) is reduced or accounted for by the prediction model. SSt is the sum of squares that would result if we had no pridiction model and had to use our best guess, which would be the mean, to create a regression line. SSe represents the sum of squares of the error produced when we use our prediction model, which, if good, will be less than SSt. The advantage of the the prediction model is the extent to which we make less error using it than if we used the mean. Subtracting SSe from SSt gies the amount that error was reduced by using the prediction model. Dividing this by SSt, the total amount that it could be reduced, gives the proportianate reduction in error and indicates the accuracy of the model.
predicted Y value (y hat)= 1.025 - .573x y hat= .509 The woman will contribute a proportion of .509 of the housework b=(-.9)(.14/.22)=-.573 a=.75-b(.48)= 1.025
StudentID: 101278100
Nickname: skibum
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 3:23:46 PM
it is because the equation is the difference between the sum of the squared deviations minus the sum of the squared error in proportion to the sum of the squared deviations. It gives you the difference between the deviations of the numbers and then the squared error ( which is the amount that a point lies off of the line of regression) and then once you divide that by the Sum of the squared deviations you will get the proportionate reduction of error, or the amount of variance that you accounted for.
You need to do several things in order to answer this problem. You need to find A, B and then finally Y^. To get A you use the equation A= My - b (Mx) and then B = Beta(SDy/SDx). the equation for B looks like this B= -.90 (.14/.22) = -.5727 A= .75-(-.57)(.48) = 1.02. Finally Y^ is Y^=a+b(x) or Y^=1.02+(..5727)(.90)=.50457. Which means that the working married woman would put forth .50 of the contribution to housework.
StudentID: 101337519
Nickname: Trixy
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 3:52:14 PM
Since r^2 is the percent of variance of the criterion variable, represented by y, explained by the predictor variable, represented by x, it makes sense that this would be equal to (SSt-SSe)/SSt because SSt is the sum of the squared deviations of Y and SSe is the sum of the squared errors between Y and the predicted value of Y. When subtracting the two and then dividing by SSt you are finding the percent of variance between the y variable explained by the x variable.
Raw score prediction equation: Y(^) = 1.02 + (-.57)(x) If the woman contributes a proportion of .90 of the household income then the proportion of the housework contribution a woman would make would be .51.
StudentID: 56695
Nickname: figure8
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 4:09:58 PM
The formula would equal the proportionate reduction in error because the calculation is a comparison. It is a comparison of the squared error using the prediction model to the squared error without use of the model.
b=-.579, a=1.0279, y=a+b(X) y=1.0279+ -.579(.9)=.5068 or .51
StudentID: 101905648
Nickname: rygy
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 5:33:18 PM
The formula (SSt - SSe)/SSt is equal to the proportionate reduction in error (r2) because they both measure the same thing. The proportionate reduction in error(r2) is also the proportion of a kind of variance that is reduced(SSt-SSe/SSt).
The equations needed to do this problem are as follows:y^= a + b(x) b= B(SDy/SDx) a= My- B(Mx) In finding b I did the following: b= B(SDy/SDx) b= -.90(.14/.22) b= -.57 In order to find a I did the follwoing: a= My - b(Mx) a= .75 - (.57)(.48) a= 1.02 In order to solve for y^ I did the following, where x=.90: y^= a + b(x) y^= 1.02 + (-.57)(.90) y^= .507 I would predict that a women who contributes a proportion of .90 of the household income to also contribute a proportion of about .507 to the housework.
StudentID: 101847140
Nickname: tigerlily
Q3: C
Honorcode: 1
Date: 2/24/00
Time: 6:07:28 PM
SSt is the total sum of squares. It is the sum of the squared differenced between each score and the overall mean of all scores; the same as sum of squared deviations from the mean (SS). SSe is the sum of squared errors. It is the sum of the squared differenced between each score and its predicted score. When using the formula (SSt - SSe)/SSt, you are finding the proportionate reduction in error, also represented by r^2. r^2 is the percent of variance that is explained by the predictor. Also the proportionate reduction in error is sometimes referred to as the proportion of variance accounted for. This is used because SSt is a kind of measure of variance of the dependent variable. Proportionate reduction in error is how much of SSt is reduced (accounted for) by the prediction model. Therefore, proportionate reduction in error is also the proportion of a kind of variance that is reduced.
r = -.90 b = r(SDy/SDx) a = MY - b(MX) SDy = .14 b = -.90(.14/.22) a = .75 - (-.5727)(.48) SDx = .22 b = -.5727 a = 1.02
estimated Y = a + b(X) Y = 1.02 + -.5727(.90) Y = .50 A woman would contribute about 50% of the housework if she contributed .90 or 90% of the househould income.
StudentID: 101169420
Nickname: quackers
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 6:14:13 PM
Because both of these equations give you the percent of variance in the criterion variable explained by the predictor variable (the percent of variance or erroe explained).
^y= a+b(x) ^y=.14 + .573(.48) b=-.90(.14/.22) ^y=.42 + -.573(.90) ^y= -.0957 the negative answer is fine b/c of the negative relationship between the variables.
StudentID: 100936160
Nickname: littlebug
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 6:59:32 PM
The proportionate reduction in error, which is the proportion of variance accounted for, equals (SS total- SS error)/SS total. The reason for this is "because SS total is a kind of measure of variance from the dependent variable's mean and is closely related to the variance of the dependent variable" (SS total/n=variance). The proportionate reduction is error is actually measuring how much SS total is reduced by the prediction model, which SS error is the sum of squared error using the prediction model.
I started by using the formula b=beta(SDy/SDx). For beta, I used -.90, which is equal to r, then I simply plugged in the values given for the standard deviations: so my equation looked like b= -.90(.14/.22), which gave me b= -.58
My next step was to solve for a, by using a=My - b(Mx). So I plugged in the variables and came up with 1.03.
My last step was to solve for the prediction of what proportion of the housework a women would make if she contributes a proportion of .90 of the household income. To come up with this figure, I used the equation Y= a+b(x), and I used .90 as the x value. My final prediction of what proportion of the housework a women would make if she contributes a proportion of .90 of the household income is .508.
StudentID: 101105091
Nickname: sly
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 7:04:38 PM
SS(total) is the total squared error when predicting from the mean is the error you get if you predict the mean of the y scores from the y score. SS(error) is the amount of error in prediction when you use the regression line to predict the y scores. Therefore, the proportionate reduction in error is the proportion of the total variance that is accounted for by using the regression line to make predictions.
B=-.90 b=-.57 a=1.02 ---> y=1.02+ (-.57)x If a woman contributed a proportion of .90 of the household income, the prediction of her proportion to the housework would be .51
StudentID: 100996799
Nickname: tank
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 8:03:02 PM
The proportionate reduction in error always equals the correlation coefficient squared. Because of this equivalence, r^2 is typically used as the symbol for the proportionate reduction error. Also, r of .4 signifies a stronger linear correlation than an r of .2. Proportionate reduction error is how much of SS total is reduced, or accounted for, the prediction model.
.90(.14/.22)=.90(.636)=.57 a=.75-(.57)(.48)=.75-.27=.48 y=.48+(.57).90=.48+.513=.993
StudentID: 101133209
Nickname: Elon
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 8:11:14 PM
The above formula explains the proportionate reduction in error because we are finding the the squared error that we are likely to find in our prediction model of the variable to the amount of squared error that we would find in our predictions without the model. In order to do this we find the amount of squared error that we would have if we make our predictions based on the model, and then find the amount of squared error we would find if we made the predictions without the model, and finally we compare that to the two squared amounts. By doing this we find the percent to which the criterion variable or the Y variable can be explained by the predictor variable or the X variable. In addition, when we are finding the amount of squared error when predicting without a model it is the same thing as if we found the amount of squared error when predicting each score to be the mean.
In this situation, the predicted value or predicted proportion of housework will equal the y-intercept and regression constant plus the slope and raw score coefficient multiplied by X or in this case a woman's income proportion of .90. To find the slope we multiply r times the (standard deviation of Y/ the standard deviation of X). In this case that number is -.57. Then we find the y-intercept which is done by taking the mean of the Y's and subtracting the slope (-.57) times the mean of the X's. The number in this case the y-intercept is 1.02. Therefore the predicted Y= 1.02+-.57(X). Therefore to find the predicted proportion of housework for a woman who has a proportion of .90 income we, plug those numbers into the formula and the result is that ther proportion of housework is .51.
StudentID: 100747476
Nickname: goat
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 8:31:20 PM
The purpose of the equation is to compare the amount of squared error we are likely to have using the prediction model t othe amount of squared error without the model. The get SSe, you add up the quared errors for each individual. For SSt, you add up the quared errors using the mean as the predicted error. It isa better measure of prediction since the proportion of squared error is reduced. r^2 is equal to this because the formula is a kind of measure of variance from the mean; this in turn is a proportionate reduction in error which = r^2.
Zx= (X=Mx)/SDx = (.90-.48)/.22 = 1.91 Zy = (X=My)/SDy = (.90-.75)/.14 = 1.07 Z^ y = B(Zx) B=-.9
Y^= (SDy)(Z^ y) + My = (.14)(-.9*1.91) + .75 = .51
I predict that a women who contributes .90 of household income would contribute .51 of the housework according to the calculations above.
StudentID: 100959428
Nickname: butterfly
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 8:56:09 PM
That formula would equal the proportionate reduction in error because you first find the reduction in error by (SSt-SSe) and then that number is divided by the total amount that could be reduced (SSt). So it equals the proportionate reduction in error because the reduction in error is being divided by the total that could be reduced which makes it a proportion.
y^=.4764+.57(x) is the raw score prediction equation.
StudentID: 100652169
Nickname: monkeydoodle
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 9:02:04 PM
The total sum of squares is the sum of the squared differences between each score and the overall mean of all scores. The sum of squared errors is the sum of the squared differences between each score and its predicted score. The proportionate reduction in error, r^2, can be explained by the formula [(SStotal-SSerror)/(SStotal)] for the same reason that r^2 is also called the proportion of variance accounted for. The proportionate reduction in error is how much the total sum of squares is reduced by the prediction model. SStotal is also a kind of measure of variance from the dependent variable's mean that is closely related to the dependent variable's variance. (pg.113 of the text)
The raw score prediction equation is y hat=a+b(x). The first step in this equation is to find b. To find b we first divide the standard deviation of y, .14, by the standard deviation of x, .22, and we get .636. We then multiply .636 by r (r=-.90) and we find that b equals -.57. The entire formula to find b would like this: b=(-.90)(.14/.22)= -.57. Now that we have b we can find a. First we multiply b times the mean of x, .48, and we get -.274. We then multiply this number times the mean of y,.75, and we find that a equals -.205. The entire formula to find a would look like this: a=[.75]-[(-.57)(.48)]= -.205. To make a prediction of what proportion of housework a woman would make if she contributes a .90 proportion of income, we would put a, b, and x into the raw score prediction equation and find that y hat=[(-.205)+(-.57)][.90]= -.72. Our prediction woud be that a woman would make a proportion of -.72 of the housework if she contributes a proportion of .90 of the household income.
StudentID: 100632956
Nickname: froggy
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 9:15:58 PM
SSt is the total squared error when predicting from the mean. This is found when one cannot use a predictor model because they no nothing of the predictor variable. The mean is used as the predictor score. SSe is the sum of squared errors. This is used when there is a prediction model available. By subtracting SSe from SSt and dividing by SSt one obtains the proprotionate reduction in error. This is always equals the correlation coefficient squared. This occurs because one is really finding the variance of the data.
The raw score prediction equation is the predicted value of Y = a + bX. The raw socre regression coefficient is b, and the regression constant is a. To find b you multiply beta(which equals the correlation coefficient)by the standard deviation of X by the standard deviation of Y. In this problem b is (-.90)(.22/.14)= -1.41. To find a you take the mean of Y and subtract it from the product of b times the mean of X. Here a is .75 - (-1.41)(.48)= 1.43. The X in the raw score prediction formula is .90 because that is predictor variable for the Y score we are trying to predict. By plugging the above numbers in to the formula 1.43 + (-1.41)(.90) we get .404 for the predicted proportion of housework for those women who contribute a proportion of .90 of the household income.
StudentID: 101835826
Nickname: Lightning Bolt
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 9:50:05 PM
SStotal is an anyalysis of the variance, the sum of squared differences of each score from the predicted score when prediciting from the mean. Proportionate reduction in error is the reduction in squared error expressed as a proportion of the squared error when using the mean to predict. In other words, proportionate recduction in error can also be called proportion of variance accounted fo which means its an indicator of effect size in an analysis of variance. Therefore, the formula would equal r^2 because they are both analyizing the variance.
Beta is equal to (r=-.90). For X(household income) : M= .48 SD= .22 For Y(housework): M=.75 SD=.14 Using the raw score prediction equation: b= Beta (SD of Y/SD of X) = (-.90)(.14/.22) = -.567 a= mean of Y- (b)(mean of X) = .75-(-.567)(.48) = 1.02 If a woman contributes a .90 of the household income, the predicted amount of housework she does is: the estimated Y = a+(b)(X) = 1.02 + (-.567)(.90) = .51
StudentID: 100982563
Nickname: Yoda
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 9:58:21 PM
SStotal is the same as finding the various of a dependent variable. SSerror represents the squared error, found by predicted Y from actual Y and squaring, the same concept you would use to find the error in an equation with just X and Y variables. Since these variables are synonimous with previously used concepts they should and do you yield the same value, proportionate reduction in error, or r squared. The book states on pg. 113 that the proportionate reduction in error is also called the proportion of variance accounted for. This is used because SStotal "is a kind of measure of variance from the dependent variable's mean and is closely related to the variance of the dependent variable." Because these variables are so closely related they will produce the same results.
First, I need to find b by taking .14/.22 and multiplying that by -.9 to get a score of -.576. To find a I take the b value of -.576 and multiply it by Now, I take that number and multiply it .48, the mean of x and add that to the mean of y, .75 for an a valua of 1.03. Now, to find the predicted y given the x value I take -.576 and multiply it by x, .9 and add that score to my a 1.03 to get a predicted y value of .51. In conclusion, if a woman contributes a proportion of .9 of the household income, it is predicted that she will contribute a proportion of .51 of the housework.
StudentID: 101115311
Nickname: scoobs
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 10:02:49 PM
R^2 or the proportionate reduction in error tells us the percentage of variance that can be explained by the predictor variable. The SST or sum of the squared total gives the amount of total squared error when predicting each score to be the mean. We can compare this to the SSE or the sum of squared error when using the prediction model. By comparing the SST to SSE we can see if there is an advantage in using the prediction model to predict our Y variable over using the mean. We determine this by seeing which sum is smaller(shows less error). In other words, if the prediction model is good SSE should be smaller than SST. By subtracting SSE from SST we calculate the reduction in error in using the prediction model. By dividing this number by the SST we get the proportionate reduction in error(r^2). The better the prediction model, the smaller SSE will be than SST. This will result in a higher percentage for the r^2. In the same way a bad prediction model will be reflected in a large SSE and therefore a small or even negative r^2.
b= -.9(.14/.22)=-.573 a= .75-(-.573)(.48)=1.025 y= 1.025-.573x when x=.9, y=1.025-.573(.9)=.509
StudentID: 100951026
Nickname: shera
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 10:09:02 PM
The proportionate reduction in error, or r^2, equals (SST-SSE)/SST. The proportionate reduction in error is defined as the percent of variability explained by the predictor variable. r equals the srength or degree of a linear relationship- with larger values of r indicating higher correlation. by squaring r, it takes into account positive and negative correlations and compares them as just high or low correlations. SST equals the sum of squares total, or in other words, the of the sum of the variances - It stands for the sum of squares when predicting using means - [(Y-mean)^2] . SSE equals the sum of squares when using the predictor model and the predictor Y^. SSE equals (Y-Y^)^2. It makes sense that subtracting the sum of squares error(using the mean) from the sum of squares total and then dividing by the sum of squares total would be finding the accuracy of the prediction model compared to using the means. this accuracy or error that is found is thus known as the proportionate reduction in error or r^2.
b= - .9 (.14/.22) = - .573
a= .75 - .48(- .573) = 1.025
Y^ = 1.025 +- .573(X)
Y^ = 1.025 +- .573(.90) = . 509
StudentID: 101220954
Nickname: Nash
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 10:44:18 PM
The proportion reduction in error gives us the percentage of reduction in error from the prediction model over using the mean to predict. The proportionate reduction in error always equals the correlation coefficient squared. The line based on the prediction model is generally closer to the dots than the line based on predicting from the mean. The proportionate reduction in error can be thought of as the extent to which the line's accuracy is greater than the horizontal line's accuracy. The difference between each actual score and what would have been predicted for that particular individual using the prediction model is called error. Squaring these errors and summing them gives the sum of squared errors (SS error). THere is also the sum of squared error when using just the mean of the dependent variable as your predicted score (SS total). The reduction in squared error using the model divided by the squared error when prediction from the depended variable's mean is called this proportion reduction in error. A correlation, or coefficient or the degree of linear correlation between variables is the average of the cross-products of the Z scores. A correlation is usually based on scores taken from a particular group that is intended to represent some larger group. For all practical purposes, the comparisons of the degree of linear correlations (correlation coefficient=r) are considereed most accurate in terms of the correlation coefficient squared (r^2). Both of these measures r^2 and proportionate reduction in error are essentially measures of how well a line fits or how making predictions about that relationship or how one score relates to a variable etc.
b=(-.90)(.14/..22)=-.57, a=.75-(-.57)(.48)=1.02, raw-score prediction equation=^Y=1.02+(-.57)(X), ^Y=1.02+(-.57)(.90)=.51. The women would make a proportion of .51 if she contributes a proportion of .90 of the household income in this negative relationship of household income and housework.
StudentID: 101816052
Nickname: chou-chou
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 10:45:43 PM
When (SSt-SSe)/SSt is calcualted, the result is that the proportion of variance accounted for is showing how much the total Sum of Squares is reduced, or accounted for, by the prediction model. This concept means that the equation shows how much of the variability in the dependant variable is accounted for by the independant variable. According to this definition, it fits exactly with the meaning of r-squared. r-squared, by finding the square of the average of the cross products of the z scores of x and y, is the percent of variance (or error) explained. This means that these two terms are synonymous.
y=a+bx b=r(SDy/SDx)=-0.90(0.14/0.22)=-0.57 a=My-b(Mx)=0.75-(-.057)(0.48)=1.03 y=1.03-0.57x y(.90)=1.03-0.57(.90)=0.51 The predicted proportion of the amount of housework a woman would contribute if she contributes a proportion of 0.90 of the household income is 0.51.
StudentID: 101974684
Nickname: buttercup
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 10:53:46 PM
The proportionate reduction in error (r2) is defined as the percent of variance (or criterion) explained by the predictor variable. In other words, it is the proportion of the variance accounted for. To find r2, the actual reduction in error must be found. This is done by subtracting the sum of squared errors from the sum of squared totals. The sum of squared errors is the "sum of the squared differences between each score and its predicted score." The sum of squared totals is "the total squared error when predicting from the mean." With this result, "the amount of squared error reduced by using the prediction model, is divided by the total amount that could be reduced," which is the sum of squared totals. Because using the mean is not a accurate method since it allows a lot of error, the prediction rule reduces the amount of error in the proportion of the squared error.
In order to make a prediction, the a and b values must be found first. In order to find b, one must multiply the beta value (which is the equivalent of r) by the result to dividing the SD of Y by the SD of X. In this case, b= -.90 (.14/.22)= -.57. After this, the a value must be calculated. To do this, subtract the product of the b value and the mean of X from the mean of Y. For this example, a= .75-(-.57)(.48)= 1.02. Finally, to find the predicted value, add a to the product of b and the given predictor. For this problem, Y^= 1.02+ -.57(.90)= .507. So, the predicted proportion of the housework a woman would make if she contributes a proportion of .90 of the household income is .507.
StudentID: 101566449
Nickname: Peaches
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 11:00:12 PM
(SSt-SSe)/SSt would equal the proportionate reduction in error. This number is a better indication than just using the mean because it lessens the error. You are taking the Error squared of a know sample and subtracting the error squared of a predicted sample and then dividing it all by the Error squared of the known sample. This number is how much of SSt is reduced or accounted for, by the prediction model.
r=-.9, Mx=.48, SDx=.22, My=.75, SDy=.14 b=SDy/SDx , .14/.22= .64 a=My-b(Mx), .75-.64(.48)=.45 y=a+b(x), .9=.45+.64x, x=.7
StudentID: 100881989
Nickname: scrubski
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 11:13:20 PM
SSt - SSe is equal to the difference between our predicted values and the actual values, divide this by the actual values (SSt) and you get your error just like in a chemistry class.
Y^ = 1.02-.57(X) and 51% of the housework.
StudentID: 101175223
Nickname: rodimus
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 11:16:53 PM
predicting the error from the mean is not as accurate as the prediction model. by using this equation we can find the proportion of how much more accurate (%) the prediction model is.
y=y hat for this problem since i can't do it on the computer. y=a+bx b=B[SD(y)/SD(x)] b=-.90[.14/.22] b=-.57 a=M(y)-bM(x) a=.75-(-.57)(.48) a=1.02 y=1.02+(-.57)x y=1.02-.57(.9) y=-4.11
StudentID: 100986806
Nickname: suzyq
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 11:17:50 PM
The proportionate reduction in error is also known as the proportion of variance accounted for. The SS total is a measure of variance from the dependent variable's mean and the SS error is the squared errors for all the individuals in the study. Using these amounts we can indicate the accuracy of the prediction model which is the proportionate reduction in error. We use these numbers because we need to know a) the reduction in error (the difference between the squared error predicting from the mean)--known as SStotal b) the squared error using the prediction model (SS error) and then the result is divided by the total amount it can be reduced by (SStotal)
I used the equation Y=a+bX b = (-.90)(.14/.22)=-.57 a=My-(b)(Mx) a=.75-(-.57)(.48)=1.02 Y=(1.02)+(-.57)(.90)=.51
StudentID: 101435626
Nickname: Vokamis
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 11:49:01 PM
Squaring r would equal the equation because (by comparing the error we would have made by using the prediction model to the error we would have made using the prediction from the mean model) it would indicate the accuracy of the prediction model. Percentage of variance of the criterion explained by the predictor.
b=-.90(.14/.22)=-.57 a=.75-(-.57*.48)=1.11 Ý=1.11+(-.57*.9)=.6
StudentID: 10190628
Nickname: smurf
Q3: D
Honorcode: 1
Date: 2/24/00
Time: 11:56:43 PM
asg
The raw-score prediction equation: y^=a + b(x) To find the slope 'b': b=SDy/SDx To find the y-intercept 'a': My - b(Mx) b= -.58 a= 1.03 and .90 will be used for x The proportion of housework a woman is predicted to contribute to if she she accounts for .90 of the household income: y^=.51
StudentID: 101125631
Nickname: Monkeygirl
Q3: A
Honorcode: 1
Date: 2/25/00
Time: 12:03:58 AM
Because they are both telling you how much of SS(total) is reduced by the prediction model
Y-cap= a + (b)(X) = 1.0236+(-.5727)(.90)=.51
StudentID: 101137818
Nickname: giggle box
Q3: D
Honorcode: 1
Date: 2/25/00
Time: 12:09:03 AM
no idea
don't I need to know the x and y values in order to calculate the raw-score prediction? Otherwise I have no idea how to do this one.
StudentID: 101852531
Nickname: Daisy Girl
Q3: D
Honorcode: 1
Date: 2/25/00
Time: 12:39:35 AM
I wish that I knew the answer, but I don't. I would just leave this question blank, but it will not allow me to submit my answers without answering this question. My answer is: you told me that this is how is works and I respect your level of knowledge on the subject and therefore refuse to question it. (sorry, just trying to brighten your day with a little joke!)
The raw-score prediction equation is predicted Y = .318 + .57 X and for a women contributes a proportion or .9 of the household income, is predicted to contribute .831 to the housework.
StudentID: 100710111
Nickname: goose
Q3: A
Honorcode: 1
Date: 2/25/00
Time: 12:48:03 AM
We know that SSe is the amount of squared error using the prediction model and that SSt stands for the sum of total squared error when predicting from the mean (the sum of the squares of the actual scores minus the mean). Proportionate reduction in error is the comparison between SSt and SSe. It is an indicator of the accuracy of the prediction model. So when you take the difference between SSt and SSe, you get the amount of squared error reduced by using the prediction model. Divide this by the total amount that could be reduced (SSt) and it gives you the proprtionate reduction in error. This is the same thing as the correlation coefficient squared.
The raw-score prediction equation would be y^=1.02+(-).57x. My prediction of the housework a woman would make is a .507 proportion. I simply plugged .90 into the y^ equation and calculated a prediction.
StudentID: 101244082
Nickname: apple bum
Q3: D
Honorcode: 1
Date: 2/25/00
Time: 12:48:47 AM
SSe (sum of the squared error) is the summation of the squared error by using the prediction model. To find it you add up the squared errors for all the individuals in the study. And when the prediction model is not available, the most accurate prediction would be to predict the mean for everyone. When the predictied score is the mean, error is the actual score minus the mean -- the squared error is the square of this number. The sum of these squared erros is the SSt (total squared error). Proportionate reduction in error (r2) is the SSt minus SSe, and the total of that is divided by the SSt. But using the mean is not a very precise method because it produces a lot of error.
b = B(SDy/SDx) = -.90(.14/.22) = -.57 a = My-b(Mx) = .75-(-.57)(.48) = .4764 Yhat = .4764 - .57x If a women contributes a predicted proportion of .90 of the house hold income, we can predict that the women would make -- Yhat = .4764 - .57(.90) = -.0363
StudentID: 101176381
Nickname: scooter
Q3: D
Honorcode: 1
Date: 2/25/00
Time: 12:51:38 AM
*The sum of squared errors (SSe) is the sum of the squared differences between each score and its predicted score. *The sum of squared errors total (SSt) is the sum of the squared differences between each score and the overall mean of all the scores. --The formula would equal the proportionate reduction in error(r2) because it is the the differences from the squared error predicitng from the mean(SSt) and the squared error using the prediction model(SSe). The number you get is the amount of squared error reduction using the prediction model, and is divided by the total amount that could be reduced (SSt). This is equal to r^2 because they are both the proportions of variance accounted for.
*Raw Score prediction variable=Y^=a+(b)X b=r(SDy/SDx) b= -.90(.14/.22) b= -.57 a=My-b(Mx) a= .75-(-.57)(.48) a=1.02 Y^= 1.02+(-.57)(.90) Y^= .507 * Based on this answer, I would predict that a woman who contributes a proportion of .90 of the household income would contribute a proportion of .507 of the household work.
StudentID: 101926649
Nickname: shakaspara
Q3: D
Honorcode: 1
Date: 2/25/00
Time: 12:58:09 AM
Both the correlation coeffecient and the formula for the proportionate reduction in error measure distance. The correlation coefficient measures the average relative placement of the 2 scores on the nomral curve, while the proportionate reduction in error measures the distance from the scores from the predicted line and from the mean line.
Y=b+ax a=r so Y=b-.9X b=r(SD of Y/SD of X) -.9(.22/.14)=-1.414 Y=1.414-.9X X=.9 Y=1.414-.9(.9)=.604
StudentID: 100879061
Nickname: brianimal
Q3: A
Honorcode: 1
Date: 2/25/00
Time: 1:01:05 AM
Proportionate reduction in error is also called proportion of variance accounted for. This is because SSt is a measure of variance from the dependent variable's mean which is close to the variance of the dependent variable. (SSt is the same thing as the SS we use to measure variance) Since proportionate reduction in error is the amount of SSt accounted for, it is also the proportion of variance that is reduced. We usually use the correlation coefficient (r) squared as the symbol for proportionate reduction in error and use the other formula when using proportion of variance accounted for. Thus, they are equal.
To find the raw score prediction equation, you first have to generate a value for b which is -.57. The next step is to generate a value for a which is 1.02. Then using the formula y=a+bx we get a raw score prediction equation of y = 1.02 - .57x. To find a propotion of housework a women would make if she contributes a proportion of .90 of the household income, you substitute .90 in for x. In doing this, the value is .51.
StudentID: 101274025
Nickname: SA
Q3: D
Honorcode: 1
Date: 2/25/00
Time: 1:01:54 AM
The proportionate reduction in error is an indicator of the accuracy of the prediction model; the percent of variance of the criterion explained by the predictor. The SSt is the sum of squared error when predicting from the mean, whereas the SSe is the sum of the squared error for that specific model. When you divide the SSe by SSt that would give you the percent of error for that model. However, when you subtract the SSe from SSt, that allows you to calculate a percentage rate for reduction between the model and the total.
The raw score prediction formula is Y(^)= a + (b)(x). From my calculations, a = 0.475; b = 0.572. And I don't quite know the rest of this, so I shall stop here.
StudentID: 101250465
Nickname: Pebbles
Q3: D
Honorcode: 1
Date: 2/25/00
Time: 1:12:55 AM
SS total is the sum of the squared deviations of each score from the overall mean of all scores and SS error is the sum of the squared differences between each score and its predicted score. Because you can also find r squared by finding r and then squaring it, this method seems to be better because there is less error because you are not using a mean. Here it is easier to find a more precise answer because if SSerror and SS total are equal it will give you a 0% for your answer.
b is equal to .573 because b=beta (SDy/SDx). Since beta is equal to r the equation is .90(.14/.22), which is equal to .573. a is equal to .475 because a=My-b(Mx). so a=.75-.573(.48), which equals .475. So the raw-score prediction equation is Ycap=.475 + .573x. Making a prediction of x=.9, the answer would be .9907. Because you substitute .90 in the equation for x.
StudentID: 101099628
Nickname: smurf
Q3: D
Honorcode: 1
Date: 2/25/00
Time: 1:13:26 AM
The indicated formula above would equal the proportionate reduction in error(r2)because both give the percentage of variation in y's that is explained by the estimated regression relationship.
Raw-score prediction equation: y^= a + b(x) Y^= 1.03 + -.58(.90) Y^= .51 For women who accounted for .90 of the household income thier contribution to house work was .51
StudentID: 101385622
Nickname: Kit Kat
Q3: D
Honorcode: 1
Date: 2/25/00
Time: 1:29:34 AM
I don't know.
In this case, b is equal to -.57. I got this by multiplying r by the standard deviation of y over the standard deviaition of x. The mean of y minus b times the mean of x (or a) is 1. The expected y value is equal to a plus b times the x value. This equation is 1+-.57*x. When I plugged in .9 for x, I got .49. One could expect this woman to contribute to 49 percent of the housework.
StudentID: 100689400
Nickname: Chip Douglas
Q3: D
Honorcode: 1
Date: 2/25/00
Time: 1:54:31 AM
The formula would equal the proportionate reduction in error (r squared) since both are measures of the association between variables. In the formula, SS(Total) is a measure of the variance from the dependent variable's mean and is close to the actual variance of the dependent variable. This is known as the proportion of variance accounted for. The formula is also equal to the proportionate reduction in error(r squared) in that it is the proportion of a kind of variance that is reduced. By using the formula, the proportion of the squared error you would make using the mean is reduced by using the prediction rule.
X= Household income Y= Housework M(Sub X)= .48 M(Sub Y)= .75 SD(Sub X)= .22 SD(Sub Y)= .14
Beta=r= -.90 b=(Beta)(SD(Sub Y)/(SD(Sub X)) b=(-.90)(.14/.22) b= -.57
a= M(Sub Y) - b(M(Sub X)) a= .75-(-.57)(.48) a= .75+.27 a= 1.02
Predicted Value of Y= a+(b)(X) = 1.02+(-.57)(.90) = 1.02 -.51 = .51
StudentID: 101229881
Nickname: Artee
Q3: D
Honorcode: 1
Date: 2/25/00
Time: 2:00:06 AM
SSt stands for the sum of squared deviations and SSe equals the sum of squared errors, when we subtract the two we find the amount of squared error reduced by using the prediction model, then when divided by the sum of squares we are dividing by the total amount that could be reduced.
I found a=.99 and b=-.52, and then when i plugged in the numbers to find Y (cap) , i found it to equal .532, but i am slightly confused as what to do next. I found .532 by adding a to b(x). For X i used .90.
StudentID: 101921521
Nickname: sweets
Q3: D
Honorcode: 1
Date: 2/25/00
Time: 2:02:41 AM
The proportionate reduction in error is sometimes called the proportion of variance accounted for. To calculate the proportionate reduction in error you use the formula SST-SSE/SST. The number that you get shows the how much of the variability in the dependent variable is accounted for by the independent variable. The proportionate reduction in error is also the proportion of a kind of variance that is reduced. r^2 is the correlation coeffcient squared. It is found by the square of the average of the cross product of z scores of X and Y. It is the percent varience, therefore, the can be used in place of the SST-SSE/SST.
Beta = r = -.9 b = beta(SDy/SDx) -.9(.14/.22) -.57 a = My - b(Mx) (.75) - (-.57)(.48) 1.0236 Y = a + b(x) 1.0236 + (-.57)(.9) * .5106 *
StudentID: 101264596
Nickname: droopy
Q3: B
Honorcode: 1
Date: 2/25/00
Time: 2:08:49 AM
?
StudentID: 100987465
Nickname: Boomer
Q3: D
Honorcode: 1
Date: 2/25/00
Time: 2:20:52 AM
SS(T) is the total squared error when predicting from the mean and SS(E) is the sum of the squared errors. SS(E) should be smaller than SS(T). By subtracting the sum of the squared errors from the sum of the total squared equals the reduction in error. This value is the amount reduced as seen in the prediction model. To find the proportionate aspect, the reduction in error is divided by SS(T). This is equal to the proportionate reduction in error, which overall was found by calculating the errors of prediction in, giving a more accurate value.
The raw-score prediction equation is Y^= a + (b) (x). To find b, then standard deviation of X is divided by the standard deviation of Y, .22/.14= 1.57. Next to find a, Mean of Y- B1(Mean of X), or .75- (1.57)(.48)= -.0036. Then these are placed back into the eqution. But, the value of x is still needed. In this particular problem, X=.90. The prediction value= 1.41.
StudentID: 101142423
Nickname: mighty mouse
Q3: D
Honorcode: 1
Date: 2/25/00
Time: 3:44:31 AM
SSE stands for the sum of the squared errors. By squaring the errors, you are eliminating the problem of having the numbers cancel each other because some are positive and some are negative. SSt stands for the total squared error when predicting from the mean. You can use that formula, SSt-SSe)/SSt because r squared always equals the correlation coefficient squared. That is what you get when you calculate the predicted scores, the error, squared errors, sums of squared errors, and proportionate reduction in squared error.
The raw score prediction equation is the correlation coefficient (B=Beta) times the standard deviation of y, the criterion, divided by the standard deviation of x, the predictor, B(SDy/SDx). The answer is -.5727. To get the predicted y-value, you have to find out what a, the regression constant is. To do that, you take the mean of y and subtract it from the raw score times the mean of x. The answer is 1.024. a= .75 - (-.5727)(.48) To get the prediction score which is y-hat, you take a and add b times x to it (y hat= 1.021 plus negative .5727 times x). If the woman contributes a proportion of .90 of the household income, it would be .2165.
StudentID: 100896105
Nickname: honeydo
Q3: D
Honorcode: 1
Date: 2/25/00
Time: 7:34:53 AM
SSe is the sum of squares erroe which is equal to E (Y- Ycap)>2 SSt is hte sum of squares total which is equal to E (Y - M)>2 R>2 is the proportionate reduction in error which means that it is the amount of variablitity of the predictor variable can be accounted for by the criterion variable. The equation (SSt - SSe)/SSt if the error is large, then the predictions made using the mean are just as good as predictions made using the prediction model. In this case SSe would be close to or exactly equal to SSt causing the numorator to be close to or equal to zero. Then, it would be divided by SSt. This means that r>2 would be close to equal to zero. Int his case either zero or close to zero percent of the variablity is explained by the variable. If the prediction model is highly accurate, then SSe is close to zero. This means that SSt-SSe is close to or equal to SSt. Then, divided by SSt, the answer is close to or equal to SSt. This means that r>2 is close to or equal to one, meaning that either 100% or close to 100% of the variance is explained by this variable.
I calculated b using b= B (SDy/SDx) = -.91 (.14/.22) = -.60 I calculated a using a = My - b (Mx) = .75 - -.60 (.48) = 1.04 Using the Equation Ycap =a + b (X)= 1.04 + -.60 (.90) = .5
StudentID: 226-25-4805
Nickname: hairball
Q3: D
Honorcode: 1
Date: 2/25/00
Time: 9:57:56 AM
The proportionate reduction in error always equals the correlation coefficient squared. r squared is usually used for proportionate reduction in error. r squared is a much simplier way of calculating proportionate reduction in error while if you use (SSt-SSe)/SSt you have to find predicted scores, errors, squared errors, sum of squared errors, and proportinate reduction in squared error.
B=-.90, b=B(SDy/SDx), b=-.90(.14/.22)=-.573, a=My-(b)(Mx), a=.75-(-.573)(.48)=1.025 B=.90, b=.573, a=.75-.573(.48)=.475 raw score prediction equation=Y capped=a+bx Y capped=.475+.573(1)=1.048