Critical Thinking: Interpreting Computer Printouts We use the form y 5 a 1 bx for the least-squares

Critical Thinking: Interpreting Computer Printouts We use the form yˆ 5 a 1 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 coeffi cient 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, shows the 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 5 11.8603 R-Sq 5 96.3%
Notice that “Elevation” is listed under “Predictor.” This means that elevation is the explanatory variable x. Its coeffi cient is the slope

b. “Constant” refers to a in the equation yˆ 5 a 1 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 coeffi cient 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 correspond ing variation in x and the least-squares line? What percentage is unexplained?