252x0772 11/26/07 (Page layout view!)ECO252 QBA2 Name ______________________ THIRD EXAM Student number_______________ November 29, 2007 Class Day and hour____________ Version 2I. (8 points) Do all the following (2 points each unless noted otherwise). Make Diagrams! Show your work! 14,27~ Nx1. 7746 xP2. 3921 xP3. 0xP4. 08.x 1252x0772 11/26/07 (Page layout view!)II. (22+ points) Do all the following (2 points each unless noted otherwise). Do not answer a question ‘yes’ or ‘no’ without giving reasons. Show your work when appropriate. Use a 5% significance level except where indicated otherwise. Note that this is extremely long and that no one will do all the problems, so look them over!1. Turn in your computer problems 2 and 3 marked as requested in the Take-home. (5 points, 2 point penalty for not doing.)2. In an ordinary 1-way ANOVA, if the computed F statistic exceeds the value from the F table at the given significance level, we cana. Reject the null hypothesis because the difference between the means is not significantb. Reject the null hypothesis because there is evidence of a significant difference between some ofthe means.c. Not reject the null hypothesis because the difference between the means is not significant.d. Not reject the null hypothesis because the difference between the means is significant.c. Not reject the null hypothesis because the difference between the variances is not significant.d. Not reject the null hypothesis because the difference between the variances is significant.e. None of the above. [7]3. After an analysis if variance, you would use the Tukey-Kramer procedure or similar confidence intervals to check a. For Normalityb. For equality of variancesc. For independence of error termsd. For pairwise differences in meanse. For all of the abovef. For none of the above4. If an ordinary one-way ANOVA has 25 columns 17 rows and 4252517 , the degrees of freedom for the F test are a. 400 and 24b. 408 and 16c. 24 and 400d. 16 and 408e. 400 and 424f. 408 and 424g. 424 and 400h. 424 and 408i. 16 and 24j. None of the above. The correct answer is _______.5. Assuming that your answer to 4 is correct and that the significance level is 1%, the correct value of F from the table is _______. (This may have to be approximate. If so, what did you use?) (1) [12]2252x0772 11/26/07 (Page layout view!)Exhibit 1 A manager believes that the number of sales that an employee makes is related to the number ofyears worked and their score on an aptitude test. He runs the data below on Minitab and gets the followingEmployee Sales Years Score 1 110 11 70 2 100 4 100 3 90 9 90 4 80 6 40 5 70 6 80 6 60 8 50 7 50 2 40 8 40 2 10MTB > regress c1 2 c2 c3Regression Analysis: Sales versus Years, Score The regression equation isSales = 28.2 + 3.10 Years + 0.470 ScorePredictor Coef SE Coef T PConstant 28.19 13.87 2.03 0.098Years 3.103 1.984 1.56 0.179Score 0.4698 0.2133 2.20 0.079S = 15.1088 R-Sq = 72.8% R-Sq(adj) = 62.0%Analysis of VarianceSource DF SS MS F PRegression 2 3058.6 1529.3 6.70 0.038Residual Error 5 1141.4 228.3Total 7 4200.0Source DF Seq SSYears 1 1951.4Score 1 1107.3The sum of the sales column is 600 and the sum of the squared numbers in the sales column is not needed.The sum of the 'years' column is 48 and the sum of the squared numbers in the years column is 362.The sum of the score column is 480 and the sum of the squared numbers in the score column is 35200If Sales is the dependent variable and years and score are the independent variables we have found that the sum of x1y is 3980 and the sum of x1 x2 is 3200. The sum of x2y has not been computed. 6. In the multiple regression, what coefficients are significant at the 10% significance level? (2)7. In the multiple regression, what coefficients are significant at the 5% significance level? (1) [15]8. Assuming that the coefficients in the multiple regression are correct, how many sales would we predict for someone with 9 years of experience and a score of 90? (1)9. Using the information in the multiple regression printout, make your result in 8) into a rough prediction interval. (2)10. Using the information in the printout, what is the value of R-squared for a regression of ‘sales’ against‘years’ alone? (2) [20]3252x0772 11/26/07 (Page layout view!)Exhibit 1 A manager believes that the number of sales that an employee makes is related to the number of years worked and their score on an aptitude test. He runs the data below on Minitab and gets the following Employee Sales Years Score 1 110 11 70 2 100 4 100 3 90 9 90 4 80 6 40 5 70 6 80 6 60 8 50 7 50 2 40 8 40 2 10MTB > regress c1 2 c2 c3Regression Analysis: Sales versus Years, Score The regression equation isSales = 28.2 + 3.10 Years + 0.470 ScorePredictor Coef SE Coef T PConstant 28.19 13.87 2.03 0.098Years 3.103 1.984 1.56 0.179Score 0.4698 0.2133 2.20 0.079S = 15.1088 R-Sq = 72.8% R-Sq(adj) =62.0%Analysis of VarianceSource DF SS MS F PRegression 2 3058.6 1529.3 6.70 0.038Residual Error 5 1141.4 228.3Total 7 4200.0Source DF Seq SSYears 1 1951.4Score 1 1107.3The sum of the sales column is 600 and the sum of the squared numbers in the sales column is not needed.The sum of the 'years' column is 48 and the sum of the squared numbers in the years column is 362.The sum of the score column is 480 and the sum of the squared numbers in the score column is 35200If Sales is the dependent variable and years and score are the independent variables we have found that the sum of x1y is 3980 and the sum of x1 x2 is 3200. The sum of x2y has not been computed.11. Do a simple regression of ‘sales’ against ‘score’ alone.a) Compute the sum xy that you will need for this regression. Show your work! (2) Don’t compute stuff that has already been done for you!b) It says that you do not need to know the sum of squares in the sales column. You do however need the spare part 22YnYSSy. Without doing any computing, tell what its value is. (1)c) Compute the coefficients of the equation xbbY20ˆ to predict the value of
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