(a) Write the equation of the least-squares regression line. Define any variables you use. (b) Interpret the slope of the regression line in context. (e) A residual plot for the regression is shown on the next page. Is a linear model appropriate for describing the rela- tionship between temperature and distance to the ncarest fish? Justify your answer.

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AP3.33. Anuclear power plant releases water into a nearby
lake every aftermoon at 4:51 P.M. Environmental research-
ers are concerned that fish are being driven away from the
area around the plant. They believe that the temperature
of the water discharged may be a factor. The scatterplot
below shows the temperature of the water ("C) released by
the plant and the measured distance (in meters) from the
outflow pipe of the plant to the nearest fish found in the
water on eight randomly chosen afternoons.
160 -
140
120
100
20
25
35
Temperature
Computer output from a least-squares regression analys
on these data is shown below.
Predictor
Coef
SE Coef
Constant
-73.64
15.48
-4.76 0.003
Temperature 5.7188 0.5612
-10.19 0.000
S= 11.4175 R-Sq = 94.5% R-Sq(adj) = 93.6%
(a) Write the equation of the least-squares regression line.
Define any variables you use.
(b) Interpret the slope of the regression line in context.
(c) A residual plot for the regression is shown on the next
page. Is a linear model appropriate for describing the rela-
tionship between temperature and distance to the nearest
fish? Justify your answer.
g sam oj a a
Transcribed Image Text:AP3.33. Anuclear power plant releases water into a nearby lake every aftermoon at 4:51 P.M. Environmental research- ers are concerned that fish are being driven away from the area around the plant. They believe that the temperature of the water discharged may be a factor. The scatterplot below shows the temperature of the water ("C) released by the plant and the measured distance (in meters) from the outflow pipe of the plant to the nearest fish found in the water on eight randomly chosen afternoons. 160 - 140 120 100 20 25 35 Temperature Computer output from a least-squares regression analys on these data is shown below. Predictor Coef SE Coef Constant -73.64 15.48 -4.76 0.003 Temperature 5.7188 0.5612 -10.19 0.000 S= 11.4175 R-Sq = 94.5% R-Sq(adj) = 93.6% (a) Write the equation of the least-squares regression line. Define any variables you use. (b) Interpret the slope of the regression line in context. (c) A residual plot for the regression is shown on the next page. Is a linear model appropriate for describing the rela- tionship between temperature and distance to the nearest fish? Justify your answer. g sam oj a a
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