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 Coef SE Coef T Constant 315.54 28.31 11.24 0.002 Elevation -28.950 3.511 -8.79 0.003 S = 11.8603 R-Sq = 96.2% 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 = 315.54 (b) For each 1000-foot increase in elevation, how many fewer frost-free days are predicted? (Round your answer to three decimal places.). ..... Enter a number. (c) The printout gives the value of the coefficient of determination . 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.) -0.9808 (d) What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? 96.2 % What percentage is unexplained? 3.8
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 Coef SE Coef T Constant 315.54 28.31 11.24 0.002 Elevation -28.950 3.511 -8.79 0.003 S = 11.8603 R-Sq = 96.2% 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 = 315.54 (b) For each 1000-foot increase in elevation, how many fewer frost-free days are predicted? (Round your answer to three decimal places.). ..... Enter a number. (c) The printout gives the value of the coefficient of determination . 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.) -0.9808 (d) What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? 96.2 % What percentage is unexplained? 3.8
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text: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.
%3D
A Minitab printout provides the following information.
Predictor
Сoef
SE Coef
P
Constant
315.54
28.31
11.24
0.002
Elevation
-28.950
3.511
-8.79
0.003
S = 11.8603
R-Sq
= 96.2%
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.
= 315.54
X x
(b) For each 1000-foot increase in elevation, how many fewer frost-free days are predicted? (Round your answer to three decimal
places.)....
Enter a number.
(c) The printout gives the value of the coefficient of determination F. 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.)
-0.9808
(d) What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line?
96.2
What percentage is unexplained?
3.8
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