we use the form y = a + bx for the least-squares line. In some computer printout

Question

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 Constant Elevation s 11.8603 SE Coef 28.31 3.511 ?? 317.43 -28.545 R-Sg- 98 . 0% 11.24 0.002 -8.79 0.003 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 ? 317.43 28.545 (b) For each 1000-foot increase in elevation, how many fewer frost-free days are predicted? (Use 3 decimal places.) 28.545 (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.) -0.972

Explanation / Answer

Given :

y^ = 317 + (-28.545)X

r2 = 98.0%

Or

r2= 0.980

Then

r = ?0.980

r = 0.990

But the sign for r based on b is negative

So,

r = - 0.990

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