the form ya + 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, metimes 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 Coef 315.00 -29.166 SE Coef (c) The printout gives the value of the coefficient 28.31 3.511 I -8.79 P 0.002 0.003 S 11.8603 R-Sq= 96.44 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 = a + bx. (a) Use the printout to write the least-squares equation. ŷ- (b) For each 1000-foot increase in elevation, how many fewer frost-free days are predicted? (Use 3 decimal places.) determination. What is the value ofr? Be sure to give the correct sign for r based on the sign of b. (Use 3 decimal places.)
the form ya + 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, metimes 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 Coef 315.00 -29.166 SE Coef (c) The printout gives the value of the coefficient 28.31 3.511 I -8.79 P 0.002 0.003 S 11.8603 R-Sq= 96.44 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 = a + bx. (a) Use the printout to write the least-squares equation. ŷ- (b) For each 1000-foot increase in elevation, how many fewer frost-free days are predicted? (Use 3 decimal places.) determination. What is the value ofr? Be sure to give the correct sign for r based on the sign of b. (Use 3 decimal places.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Transcribed Image Text:We use the form ŷ = 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
Coef
315.00
-29.166
SE Coef
28.31
3.511
I
11.24
-8.79
P
0.002
0.003
S = 11.8603
R-Sq = 96.44
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 = a + bx.
(c) The printout gives the value of the coefficient of determination
(a) Use the printout to write the least-squares equation.
ŷ =
X
(b) For each 1000-foot increase in elevation, how many fewer frost-free days are predicted? (Use 3 decimal places.)
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.)
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