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
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A Minitab printout provides |
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|
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% |
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(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?
