Chapter B, Problem 29RP

Patent Production. Refer to Problem 18, where we examined the regression analysis of the number of patents per 1000 workers on four predictor variables: workforce education score, high-tech jobs (as a share of total employment), percentage of scientists and engineers in the workforce, and investment in research and development (as a share of gross state product). We expand this regression analysis by considering data on six additional predictor variables:

• managerial, professional, and technical jobs as a share of the total workforce
• share of jobs in manufacturing companies dependent upon exports
• percentage of adults with Internet access
• score for technology use in schools
• score for the utilization of digital technologies in state governments
• venture capital invested as a percentage of gross state product

The data for these additional predictor variables are presented in the table on page B-178. Use the technology of your choice to do the following for these data.

1. a. Apply the forward selection method to obtain a regression equation. (Use t_enter = 2.00, Or α_enter = 0.05.)
2. b. Apply the backward elimination method to obtain a regression equation. (Use t_remove = 2.00, α_remove = 0.05.)
3. c. Apply stepwise regression to obtain a regression equation. (Use t_enter ⁼ t_remove ⁼ 2.00, Or α_enter ⁼ α_remove ⁼ 0.05.)
4. d. Are the regression equations that you obtained in parts (a), (b), and (c) the same? If so, is that always the case?
5. e. For the regression equation obtained in part (c) by stepwise regression, construct plots of residuals versus filled values, residuals versus the included predictor variables, and a normal probability plot of the residuals. Perform a residual analysis to assess the appropriateness of the regression equation, constancy of the conditional standard deviations, and normality of the conditional distributions. Check for outliers and influential observations.