How much does education affect wage rates? Use the following data to develop an

Question

How much does education affect wage rates? 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 education. y x WAGE EDUC 9.88 13 10.96 12 8.25 13 14.86 18 8.75 12 15.3 12 12.7 12 10.75 13 17.33 12 7.5 10 18.5 12 9 13 51.29 21 20.53 14 12.68 18 7.25 12 18.28 14 21.63 16 19.23 14 25 12 16.83 16 10.53 12 16.35 13 5.2 13 50 13 The numerator of the formula to compute the slope coefficient of the regression equation is ________. Use Excel!! 402.117 390.228 360.335 321.472 The estimated regression equation predicts that the expected wage rate for a person with 16 years of education is ______. $29.45 $25.45 $22.10 $21.08 In the sample, the observed wage data deviate from the predicted wage, on average, by $ ________. $9.89 $10.21 $12.35 $14.14 What proportion of the variations in wage can be explained by education? 0.3244 0.2862 0.2519 0.2303 The standard error of the slope coefficient is ______. 0.6822 0.8510 1.1606 1.8954 The 95% confidence interval for the population slope parameter is: 0.285 3.805 0.472 3.993 0.685 4.205 0.775 4.295 To test, at a 5% level of significance, the hypothesis H: = 0 versus H: 0, the t test statistic is
|t| = ______. 1.984 Reject the null hypothesis. 2.215 Reject the null hypothesis. 2.623 Reject the null hypothesis. 2.918 Reject the null hypothesis. How much does education affect wage rates? 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 education. y x WAGE EDUC 9.88 13 10.96 12 8.25 13 14.86 18 8.75 12 15.3 12 12.7 12 10.75 13 17.33 12 7.5 10 18.5 12 9 13 51.29 21 20.53 14 12.68 18 7.25 12 18.28 14 21.63 16 19.23 14 25 12 16.83 16 10.53 12 16.35 13 5.2 13 50 13

Explanation / Answer

A. correct answer is (d) 321.472 (= 717.6683 / 2.2324)

B. correct answer is (c) 22.10

C. correct answer is (b) 10.21

D. correct answer is (d) 0.2303

E. correct answer is (b) 0.8510

F. correct answer is (b) 0.472 - 3.993

G. correct answer is (c) 2.623 (Reject the null hypothesis)

SUMMARY OUTPUT Regression Statistics Multiple R 0.479884959 R Square 0.230289574 Adjusted R Square 0.196823903 Standard Error 10.21232283 Observations 25 ANOVA df SS MS F Significance F Regression 1 717.6683804 717.6683804 6.881367341 0.015197115 Residual 23 2398.705364 104.2915375 Total 24 3116.373744 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -13.61804444 11.75280169 -1.158706222 0.258465626 -37.93056696 10.69447807 -37.93056696 10.69447807 EDUC 2.232444444 0.851026902 2.623236044 0.015197115 0.471961176 3.992927713 0.471961176 3.992927713 RESIDUAL OUTPUT PROBABILITY OUTPUT Observation Predicted WAGE Residuals Standard Residuals Percentile WAGE 1 15.40373333 -5.523733333 -0.552522378 2 5.2 2 13.17128889 -2.211288889 -0.221188555 6 7.25 3 15.40373333 -7.153733333 -0.715566359 10 7.5 4 26.56595556 -11.70595556 -1.170911412 14 8.25 5 13.17128889 -4.421288889 -0.442248186 18 8.75 6 13.17128889 2.128711111 0.212928549 22 9 7 13.17128889 -0.471288889 -0.047141605 26 9.88 8 15.40373333 -4.653733333 -0.465498903 30 10.53 9 13.17128889 4.158711111 0.415983324 34 10.75 10 8.7064 -1.2064 -0.120672552 38 10.96 11 13.17128889 5.328711111 0.533014893 42 12.68 12 15.40373333 -6.403733333 -0.640546122 46 12.7 13 33.26328889 18.02671111 1.803157517 50 14.86 14 17.63617778 2.893822222 0.289460305 54 15.3 15 26.56595556 -13.88595556 -1.388970233 58 16.35 16 13.17128889 -5.921288889 -0.59228866 62 16.83 17 17.63617778 0.643822222 0.064399594 66 17.33 18 22.10106667 -0.471066667 -0.047119377 70 18.28 19 17.63617778 1.593822222 0.159425228 74 18.5 20 13.17128889 11.82871111 1.183190279 78 19.23 21 22.10106667 -5.271066667 -0.527248893 82 20.53 22 13.17128889 -2.641288889 -0.264200157 86 21.63 23 15.40373333 0.946266667 0.094652199 90 25 24 15.40373333 -10.20373333 -1.020648656 94 50 25 15.40373333 34.59626667 3.460560161 98 51.29

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