NAME: You 1 a 2 a 3 4 5 6 7 c 8 d 9 a 10 11 12 13 c 14 d 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 When done, using your last name and firstname, save THIS FILE as, E270Lastname Firstname HW7 Upload to Canvas > Assignments Given are five observations for two variables, x and y. y x 16 5 12 6 7 7 18 8 35 9 a b c d The value in the numerator of the formula to compute the slope coefficient b is: 44 42 40 38 a b c d The value in the denominator of the formula to compute the slope coefficient b is: 10 12 14 16 1 2 3 a b c d The value of the intercept coefficient b is: -12.8 -13.2 -13.6 -14.0 a b c d The predicted value of y when x = 8 is: 23.1 22.9 22.5 22.0 a b c d The prediction error when x = 8 is, -4.0 -4.5 -4.9 -5.1 a b c d The sum of squared errors (SSE) is, 250.0 252.8 255.6 258.4 a b c d The standard error of estimate, se(e), for the model is: 9.230 8.584 7.983 7.425 a b c d The sum of squares total (SST) is, 261.0 265.1 273.7 449.2 a b c d The sum of squares regression (SSR) is, 193.6 191.8 190.0 188.2 4 5 6 7 8 9 10 a b c d The fraction of variations in y explained by x is: 0.4072 0.4310 0.4606 0.4947 11 The measure of dispersion of the estimated slope coefficient (b) about the population slope parameter () is: se(b) = 1.960 2.152 a b c d 12 a b c d 2.663 2.919 The test statistic for the null hypothesis H: = 0 is: 2.170 1.856 1.507 0.982 Next FOUR questions are based on the following How much does education affect wage rate? Use the following data to develop an estimated regression equation that could be used to predict the WAGE for a given number of years of schooling. WAGE EDUC Note: To facilitate calculations, name the columns that contain the x and y x y data. First select the range, including the top row containing the 19.45 15 column headings, by dragging the mouse. Then click on FORMULAS tab 11.5 12 on the Ribbon. Then in "Defined Names" group click on "Create from 15.34 17 Selection" and check the "Top row" box. 26.21 13 24.99 12 20.6 12 54.38 16 26 12 29.72 16 16.83 13 15.24 11 43.25 16 19.42 11 14.42 14 8.08 12 58.85 22 21 12 21.25 17 22.66 12 69.44 14 10.71 12 10.18 13 11.4 11 8.58 13 15.16 17 13 a b c d 14 a b c d The estimated regression equation predicts that the wage rate rises by ______ for each additional year of schooling. $2.76 $2.99 $3.18 $3.72 The predicted wage for a person with 16 years of schooling is, $26.58 $27.98 $29.63 $30.78 15 a b c d The sum of squared error (SSE) is, 4649.49 4552.90 4367.51 4128.61 16 a b c d The sum of squares regression (SSR) is, 1240.77 1498.40 1558.33 1679.88 17 a b c d The sum of squares total (SST) is, 5644.25 5879.43 6232.78 6369.38 18 a b c d The observed WAGE (y) deviate from the predicted WAGE (y), on average, by, 14.07 13.49 12.68 11.07 19 a b c d The fraction of variation in WAGE (y) explained by EDUC (x) is, 0.2240 0.2695 0.3172 0.3586 20 a b c d The standard error of the slope coefficient is ______. 0.968 1.092 1.858 2.090 21 a b c d The margin of error for a 95% confidence interval for the population slope parameter is: 2.95 2.63 2.26 1.98 22 To test, at a 5% level of significance, the hypothesis H: = 0 versus H: 0, the t test statistic is |t| = ______. 1.982 2.445 2.913 3.459 a b c d Questions 23-30 are based on the computer output below relating to the following problem Pete Zaria would like to study the relationship between pizza sales and advertising. The following is the result of a regression analysis Pete conducted for monthly sales of pizza and advertising (both in thousands of dollars) The exercise involves filling in the values for the shaded cells bellow. SUMMARY OUTPUT Regression Statistics Multiple R 0.63699 R Square Adjusted R Square 0.39762 Standard Error Observations ANOVA df SS Residual Total Coefficients Standard Error Intercept ADVERT MS F Significance F P-value Lower 95% 1 73 25.3609961 74 3115.48187 Regression 66.6742 5.2282 1.6233 t Stat 41.0721 0.0000 63.4389 Upper 95% 69.9095 23 a b c d The predicted sales when $2 (thousand) is spent on advertising is: 77.13 75.31 73.65 71.20 24 a b c d The value for SSE is, 1798.3821 1801.4814 1851.3527 1895.6048 25 a b c d The observed SALES (y) deviate from the predicted SALES (y), on average, by, 3.975 4.969 5.036 6.770 26 a b c d The fraction of the variations is SALES explained by advertising is, 0.479 0.406 0.369 0.346 27 a b c d Given (x xx ) = 46.2466, the value of the standard error of the slope coefficient in (6) is: 1.685 1.250 0.983 0.741 28 a b c d The value of the t Stat to test the hypothesis that advertising has no impact on sales is, 5.788 6.682 7.060 7.946 29 a b c d The critical value, at a 5 percent level of significance, for the above hypothesis is: 2.369 2.246 2.114 1.993 30 a b c d The lower and upper ends of a 95% confidence interval for the population slope parameter are: 3.752 6.704 3.585 6.871 3.246 7.210 3.183 7.273 6 a a b d a c a d a b d c c d b d c a b b c c a c c b d c d a