Chapter 4.2, Problem 5P

Critical Thinking: Interpreting Computer Printouts We use the form $\hat{y}=a+bx$ for the least-squares line. In some computer printouts, the least- squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from Climatology Report No. 77-3 of the Department of Atmospheric Science, Colorado State University, showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in Colorado locations.

A Minitab printout provides

Predictor	Coef	SE Coef	T	P
Constant	318.16	28.31	11.24	0.002
Elevation	-30.878	3.511	-8.79	0.003

s = 11.8603 R-Sq = 96.3%

Notice that “Elevation” is listed under “Predictor.” This means that elevation is the explanatory variable x. Its coefficient is the slope b. “Constant” refers to a in the equation $\hat{y}=a+bx$.

(a) Use the printout to write the least-squares equation.

(b) For each 1000-foot increase in elevation, how many fewer frost-free days are predicted?

(c) The printout gives the value of the coefficient of determination $r^2$. What is the value of r? Be sure to give the correct sign for r based on the sign of b.

(d) Interpretation What percentage of the variation in y can he explained by the corresponding variation in x and the least-squares line? What percentage is unexplained?