The U.S. Bureau of Labor Statistics provides data on the year-to-year percentage changes in the wages and salaries of workers in private industries, including both “white-collar” and “blue-collar” occupations. Here we consider these data for the years 1980-1996 in the file P2_56.XLS. Is there evidence of a linear relationship between the yearly changes in the wages and salaries of “white-collar” (Y) and “blue-collar” (X) workers in the United States over the given time period? Begin to answer this question by estimating a simple linear regression model. 

a. Construct a 95% confidence interval for the model’s slope (i.e., β₁) parameter. Interpret this interval estimate to answer the question posed above. 

b. Interpret the ANOVA table for this model. In particular, does the explanatory variable included in this simple regression model provide at least some power in explaining the variation in the response variable? Report a p-value for this hypothesis test. 

c. What is the relationship between the computed t-ratio for the estimated coefficient of the explanatory variable and the computed F-ratio found in the ANOVA section of the output? Do these two test statistic values provide the same indication regarding a possible relationship between yearly changes in the wages and salaries of white-collar and blue-collar workers? Explain why or why not.