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Critical thinking: interpreting computer printouts

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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 *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. 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 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% |

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

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