We use the form 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 the following information.
Predictor Coef SE Coef T P
Constant 317.97 28.31 11.24 0.002
Elevation -32.325 3.511 -8.79 0.003
S = 11.8603 R-Sq = 96.2%
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 y = a + bx.
(a) Use the printout to write the least-squares equation.
y = + x
(b) For each 1000-foot increase in elevation, how many fewer frost-free days are predicted? (Use 3 decimal places.)
(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. (Use 3 decimal places.)