We use from y = a + bx for the least squares line. In some computer printouts, t

Question

We use from 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 of the climatology Report No. 77-3 of the Department of Atmospheric Science, Colorado State University, shows the relationship between (in thousands feet) and average number of frost-free days per year in Colorado locations. A provides the following information. 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. Use the printout to write the least-squares equation. For each 1000-foot increase in elevation, how many fewer frost-free days are predicted? (use 3 decimal places.) The printout gives the value of the coefficient of determination r^2. What is the value of n Be sure to give the correct sign for r based on the sign of b (use 3 decimal places.)

Explanation / Answer

(a) Regression equation is y = 318.78 - 31.866x

(b) 31.866 fewer frost-free days

(c) r^2 = 98.04%= 0.9804, so r =98.04 = 0.990

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