# We use the form = + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant is given, and the coefficient b of the explanatory

We use the form ŷ = α + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant α is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes α 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:

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 ŷ = α + bx

(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?

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 ŷ = α + bx

(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?

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