We use the form ý -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 a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. A Minitab printout provides the following information. Predictor Coef SE Coef Constant 315.81 28.31 11.24 0.002 Elevation -32.136 3.511 -8.79 0.003 S- 11.8603 R-Sq - 96.6 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 ý = a + bx. (a) Use the printout to write the least-squares equation. ý - 315.81 v + -32.136 (b) For each 1000-foot increase in elevation, how many fewer frost-free days are predicted? (Round your answer to three decimal places.) (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. (Round your answer to four decimal places.) (d) 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?
We use the form ý -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 a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. A Minitab printout provides the following information. Predictor Coef SE Coef Constant 315.81 28.31 11.24 0.002 Elevation -32.136 3.511 -8.79 0.003 S- 11.8603 R-Sq - 96.6 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 ý = a + bx. (a) Use the printout to write the least-squares equation. ý - 315.81 v + -32.136 (b) For each 1000-foot increase in elevation, how many fewer frost-free days are predicted? (Round your answer to three decimal places.) (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. (Round your answer to four decimal places.) (d) 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?
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter3: Straight Lines And Linear Functions
Section3.3: Modeling Data With Linear Functions
Problem 13SBE
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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 a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a
state.
A Minitab printout provides the following information.
Predictor
Сoef
SE Coef
T
P
Constant
315.81
28.31
11.24
0.002
Elevation
-32.136
3.511
-8.79
0.003
S = 11.8603
R-Sq = 96.6%
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.
(a) Use the printout to write the least-squares equation.
ŷ = 315.81
+ -32.136
(b) For each 1000-foot increase in elevation, how many fewer frost-free days are predicted? (Round your answer to three decimal places.)
(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. (Round your answer to four decimal places.)
(d) 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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