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CHAPTER 12. LINEAR REGRESSION AND CORRELATION
b.
r = 0.8, significant
c.
yhat = 48.40.00725x
d.
For every one pound increase in weight, the fuel efficiency decreases by 0.00725 miles per gallon. (For
every one thousand pound increase in weight, the fuel efficiency decreases by 7.25 miles per gallon.)
e.
64% of the variation in fuel efficiency is explained by the variation in weight using the regression line.
g.
yhat=48.40.00725(3000)=26.65 mpg. yyhat=2526.65=1.65. Because yhat=26.5 is greater than y=25, the
line overestimates the observed fuel efficiency.
h.
(2750,38) is the outlier. Be sure you know how to justify it using the requested graphical or numerical
methods, not just by guessing.
i.
yhat = 42.40.00578x
j.
Without outlier, r=0.885, rsquare=0.76; with outlier, r=0.8, rsquare=0.64.
The new linear model is a
better fit, after the outlier is removed from the data, because the new correlation coefficient is farther
from 0 and the new coefficient of determination is larger.
Solution to Exercise 12.27 (p. 202)
a. All four data sets have the same correlation coefficient r=0.816 and the same least squares regression line
yhat=3+0.5x
b. Set 2 ; c. Set 4 ; d. Set 3 ; e. Set 1
Figure 12.1
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 Fall '08
 Ripol
 Statistics, Correlation, Linear Regression, Regression Analysis, Variance, Javier

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