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Critical thinking: interpreting computer printouts

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We use the form width== 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 of the explanatory or predictor variable is displayed. Sometimes 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 r2. What is the value of r? Be sure to give the correct sign for based on the sign of b.

(d) Interpretation What percentage of the variation in can be explained by the corresponding variation in and the least-squares line? What percentage is unexplained?

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