A nuclear power plant releases water into a nearby lake every afternoon at 4:51 p.m. Environmental researchers 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.

Computer output from a least-squares regression analysis on these data and a residual plot are shown below.
Predictor Coef SE Coef T P 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) Is a linear model appropriate for describing the relationship between temperature and distance to the nearest fish? Justify your answer.

(d) Compute the residual for the point (29, 78). Interpret this residual in context.

Transcribed Image Text:

Distance to nearest fish (meters) 160 140 120 100 80 60 40 20 0 15 20 25 30 Temperature (C) 35 40