Question: Consider the following bivariate data that reflects a linear model:

a. Construct the linear regression model \(\hat{y}={{b}_{0}}+{{b}_{1}}x\) that corresponds to this data. [COMMENTS & HINTS: Use a calculator or spreadsheet to determine the least squares equation or line of best fit; a computational table is not necessary.]

b. Determine the Pearson product moment correlation coefficient, r. [COMMENTS & HINTS: Express the terminating decimal answer precisely, without rounding. Again, use technology to your advantage so to avoid tedious computations.]

c. What percentage of the variability is due to the linear relationship between the two variables? [COMMENTS & HINTS: Compute the coefficient of determination.]

d. If \(x=5\), what is the predicted value for y?

e. What value for x corresponds to a predicted value \(\hat{y}=-22.7\) ?