The Current Population Survey (CPS) is used to supplement census information between census years. These data consist of a random sample of 534 persons from the CPS, with information on wages and other characteristics of the workers in 2018. Some of the data is included in the file WagesData.mtw. The variables are WAGE: Hourly wage (dollars per hour) EDUCATION: Number of years of education WAGESDATA2.MTW Regression Analysis: Wage versus Education Method Rows unused 123 Model Summary SR-sq R-sq(adjPRESS R-sq(pred) AICC BIC 4.75399 14.59% 14.43% 121210 13.89% 3184.46 3197.26 Regression Equation Wage = 9.25 +0.7505 Education Analysis of Variance Coefficients Term Coef SE Coef 95% CIT-Value P.Value VIF Constant 9.25 1.05 (7.20, 11.31) 8.850.000 Education 0.7505 0.0787 (0.5958, 0.9051) 9.53 0.000 1.00 Source DF Seq SS Contribution Adj SS Adj MS F-Value P.Value Regression 1 2053.3 14.59% 2053.3 2053.29 90.850.000 Education 1 2053.3 14.59% 2053.3 2053.29 90.85 0.000 Error 532 12023.4 85.41% 12023.4 22.60 Lack-of-Fit 15 523.7 3.72% 523.7 34.921.57 0.078 Pure Error 517 11499.7 81.69% 11499.7 22.24 Total 533 14076.7 100.00% a) Interpret the 95% confidence interval for the true slope, B, associated with this least-squares linear model, include if the model is statistically useful or not. Explain. {8 points} b) Predict the hourly wage of a person who has 3.5 years of education. {4 points} c) Which is the correct interpretation of the predictor coefficient? {4 points} Answer: a. For each dollar increase in hourly wage, education will increase by .7505 years. b. For each year increase in education, hourly wages will increase by .7505 dollars. C. For each dollar increase in hourly wage, education will increase by 9.25 years. d. For each year increase in education, hourly wages will increase by 9.25 dollars. The Current Population Survey (CPS) is used to supplement census information between census years. These data consist of a random sample of 534 persons from the CPS, with information on wages and other characteristics of the workers in 2018. Some of the data is included in the file WagesData.mtw. The variables are WAGE: Hourly wage (dollars per hour) EDUCATION: Number of years of education WAGESDATA2.MTW Regression Analysis: Wage versus Education Method Rows unused 123 Model Summary SR-sq R-sq(adjPRESS R-sq(pred) AICC BIC 4.75399 14.59% 14.43% 121210 13.89% 3184.46 3197.26 Regression Equation Wage = 9.25 +0.7505 Education Analysis of Variance Coefficients Term Coef SE Coef 95% CIT-Value P.Value VIF Constant 9.25 1.05 (7.20, 11.31) 8.850.000 Education 0.7505 0.0787 (0.5958, 0.9051) 9.53 0.000 1.00 Source DF Seq SS Contribution Adj SS Adj MS F-Value P.Value Regression 1 2053.3 14.59% 2053.3 2053.29 90.850.000 Education 1 2053.3 14.59% 2053.3 2053.29 90.85 0.000 Error 532 12023.4 85.41% 12023.4 22.60 Lack-of-Fit 15 523.7 3.72% 523.7 34.921.57 0.078 Pure Error 517 11499.7 81.69% 11499.7 22.24 Total 533 14076.7 100.00% a) Interpret the 95% confidence interval for the true slope, B, associated with this least-squares linear model, include if the model is statistically useful or not. Explain. {8 points} b) Predict the hourly wage of a person who has 3.5 years of education. {4 points} c) Which is the correct interpretation of the predictor coefficient? {4 points} Answer: a. For each dollar increase in hourly wage, education will increase by .7505 years. b. For each year increase in education, hourly wages will increase by .7505 dollars. C. For each dollar increase in hourly wage, education will increase by 9.25 years. d. For each year increase in education, hourly wages will increase by 9.25 dollars
