Critical Thinking: Interpreting Computer Printouts

We use the form = a + bx for the least-squares line. In some computer printouts, the leastsquares equation is not given directly. Instead, the value of the constant ais 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. 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

(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 r². 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 be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained?