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ODB 3.17 Consider the regression model WAGE =B₁ + B₂EDUC+ e. Where WAGE is hourly wage rate in US 2013 dollars. EDUC is years of schooling. The model is estimated twice, once using individuals from an urban area, and again for individuals in a rural area. Urban Rural WAGE= -10.76 +2.46EDUC, N = 986 (se) (2.27) (0.16) 10 WAGE= (se) -4.88 +1.80EDUC, N = 214 (3.29) (0.24) mizo quods eu lis a. Using the urban regression, test the null hypothesis that the regression slope equals 1.80 against the alternative that it is greater than 1.80. Use the α = 0.05 level of significance. Show all steps, including a graph of the critical region and state your conclusion. b. Using the rural regression, compute a 95% interval estimate for expected WAGE if EDUC = 16. The required standard error is 0.833. Show how it is calculated using the fact that the estimated covariance between the intercept and slope coefficients is -0.761. c. Using the urban regression, compute a 95% interval estimate for expected WAGE if EDUC= 16. The estimated covariance between the intercept and slope coefficients is -0.345. Is the interval estimate for the urban regression wider or narrower than that for the rural regression in (b). Do you find this plausible? Explain. d. Using the rural regression, test the hypothesis that the intercept parameter B, equals four, or more, against the alternative that it is less than four, at the 1% level of significance.

ODB 3.17 Consider the regression model WAGE =B₁ + B₂EDUC+ e. Where WAGE is hourly wage rate in US 2013 dollars. EDUC is years of schooling. The model is estimated twice, once using individuals from an urban area, and again for individuals in a rural area. Urban Rural WAGE= -10.76 +2.46EDUC, N = 986 (se) (2.27) (0.16) 10 WAGE= (se) -4.88 +1.80EDUC, N = 214 (3.29) (0.24) mizo quods eu lis a. Using the urban regression, test the null hypothesis that the regression slope equals 1.80 against the alternative that it is greater than 1.80. Use the α = 0.05 level of significance. Show all steps, including a graph of the critical region and state your conclusion. b. Using the rural regression, compute a 95% interval estimate for expected WAGE if EDUC = 16. The required standard error is 0.833. Show how it is calculated using the fact that the estimated covariance between the intercept and slope coefficients is -0.761. c. Using the urban regression, compute a 95% interval estimate for expected WAGE if EDUC= 16. The estimated covariance between the intercept and slope coefficients is -0.345. Is the interval estimate for the urban regression wider or narrower than that for the rural regression in (b). Do you find this plausible? Explain. d. Using the rural regression, test the hypothesis that the intercept parameter B, equals four, or more, against the alternative that it is less than four, at the 1% level of significance.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Please solve question 3.17 in its entirety, thanks!
we should have mandatory car e. There is a saying, "Correlation does not imply causation." How might this saying relate to part (d)? f. Post hoc ergo propter hoc (Latin: "after this, therefore because of this") is a logical fallacy discussed algpris widely in Principles of Economics textbooks. An example might be "A rooster crows and then the sun appears, thus the crowing rooster causes the sun to rise." How might this fallacy relate to the observation in part (d)? 3.17 Consider the regression model WAGE =B₁ + B₂EDUC+ e. Where WAGE is hourly wage rate in Us 2013 dollars. EDUC is years of schooling. The model is estimated twice, once using individuals from an urban area, and again for individuals in a rural area. Urban Rural WAGE= (se) -10.76+2.46EDUC, N = 986 (2.27) (0.16) 10 WAGE= -4.88 +1.80EDUC, N = 214 (se) (3.29) (0.24) muze boods eu lla a. Using the urban regression, test the null hypothesis that the regression slope equals 1.80 against the alternative that it is greater than 1.80. Use the α = 0.05 level of significance. Show all steps, including a graph of the critical region and state your conclusion. b. Using the rural regression, compute a 95% interval estimate for expected WAGE if EDUC = 16. The required standard error is 0.833. Show how it is calculated using the fact that the estimated covariance between the intercept and slope coefficients is -0.761. c. Using the urban regression, compute a 95% interval estimate for expected WAGE if EDUC= 16. The estimated covariance between the intercept and slope coefficients is -0.345. Is the interval estimate for the urban regression wider or narrower than that for the rural regression in (b). Do you find this plausible? Explain. d. Using the rural regression, test the hypothesis that the intercept parameter 3₁ equals four, or more, against the alternative that it is less than four, at the 1% level of significance. 3.18 A life insurance company examines the relationship between the amount of life insurance held by a household and household income. Let INCOME be household income (thousands of dollars) and INSURANCE the amount of life insurance held (thousands of dollars). Using a random sample of N = 20 households, the least squares estimated relationship is INSURANCE = 6.855 +3.880INCOME (se) (7.383) (0.112) 3-
Transcribed Image Text:we should have mandatory car e. There is a saying, "Correlation does not imply causation." How might this saying relate to part (d)? f. Post hoc ergo propter hoc (Latin: "after this, therefore because of this") is a logical fallacy discussed algpris widely in Principles of Economics textbooks. An example might be "A rooster crows and then the sun appears, thus the crowing rooster causes the sun to rise." How might this fallacy relate to the observation in part (d)? 3.17 Consider the regression model WAGE =B₁ + B₂EDUC+ e. Where WAGE is hourly wage rate in Us 2013 dollars. EDUC is years of schooling. The model is estimated twice, once using individuals from an urban area, and again for individuals in a rural area. Urban Rural WAGE= (se) -10.76+2.46EDUC, N = 986 (2.27) (0.16) 10 WAGE= -4.88 +1.80EDUC, N = 214 (se) (3.29) (0.24) muze boods eu lla a. Using the urban regression, test the null hypothesis that the regression slope equals 1.80 against the alternative that it is greater than 1.80. Use the α = 0.05 level of significance. Show all steps, including a graph of the critical region and state your conclusion. b. Using the rural regression, compute a 95% interval estimate for expected WAGE if EDUC = 16. The required standard error is 0.833. Show how it is calculated using the fact that the estimated covariance between the intercept and slope coefficients is -0.761. c. Using the urban regression, compute a 95% interval estimate for expected WAGE if EDUC= 16. The estimated covariance between the intercept and slope coefficients is -0.345. Is the interval estimate for the urban regression wider or narrower than that for the rural regression in (b). Do you find this plausible? Explain. d. Using the rural regression, test the hypothesis that the intercept parameter 3₁ equals four, or more, against the alternative that it is less than four, at the 1% level of significance. 3.18 A life insurance company examines the relationship between the amount of life insurance held by a household and household income. Let INCOME be household income (thousands of dollars) and INSURANCE the amount of life insurance held (thousands of dollars). Using a random sample of N = 20 households, the least squares estimated relationship is INSURANCE = 6.855 +3.880INCOME (se) (7.383) (0.112) 3-
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