We use the form = 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 Coef SE Coef T P Constant 318.24 28.31 11.24 0.002 Elevation -30.327 3.511 -8.79 0.003 S = 11.8603 R-Sq = 95.8% 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 = a + bx. (a) Use the printout to write the least-squares equation. y^= ?+?x (b) For each 1000-foot increase in elevation, how many fewer frost-free days are predicted? (Use 3 decimal places.)(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. (Use 3 decimal places.)

We use the form = 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...

We use the form =
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	Coef	SE Coef	T	P
Constant	318.24	28.31	11.24	0.002
Elevation	-30.327	3.511	-8.79	0.003
S = 11.8603	R-Sq = 95.8%

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 =
a + bx.

(a) Use the printout to write the least-squares equation.

y^=

?+?x

(b) For each 1000-foot increase in elevation, how many fewer frost-free days are predicted? (Use 3 decimal places.)

(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. (Use 3 decimal places.)

Jun 03, 2022

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We use the form = 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...

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