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...


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.

































PredictorCoefSE CoefTP
Constant315.2728.3111.240.002
Elevation-31.3533.511-8.790.003
S = 11.8603R-Sq = 96.0%


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


(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
r
2. 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?

%


Jun 01, 2022
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