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 P Constant 316.89 28.31 11.24 0.002 Elevation -30.084 3.511 -8.79 0.003 S = 11.8603 R-Sq = 97.8% 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 ŷ = a + bx. (a) Use the printout to write the least-squares equation. ŷ = __+ x 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?

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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Question

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	P
Constant	316.89	28.31	11.24	0.002
Elevation	-30.084	3.511	-8.79	0.003
S = 11.8603	R-Sq = 97.8%

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

ŷ = a + bx.

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

ŷ =	______+ ____ x

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?

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