Researchers measured oxygen consumption in 10 seals both for feeding and nonfeeding dives. A regression analysis of consumption in feeding dives versus nonfeeding dives is summarized below for the model:

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 16.7693 8.6483 1.939 0.0885 . OxygenNonfeeding 1.2010 0.1124 10.681 5.18e-06 *** --- Residual standard error: 6.542 on 8 degrees of freedom Multiple R-squared: 0.9345,Adjusted R-squared: 0.9263 F-statistic: 114.1 on 1 and 8 DF, p-value: 5.18e-06

(a)Use the regression equation to estimate the oxygen consumption for a feeding dive for a seal for which the oxygen consumption in a nonfeeding dive is 80.0.

(b)Find a 95% confidence interval for the slope of the regression equation.

(c)Which is wider:

(1)a 95% confidence interval for the mean oxygen consumption in a feeding dive of all seals with a measure of 80.0 in nonfeeding dives;

(2)a 95% prediction interval for the mean oxygen consumption in a feeding dive of a single seal with a measure of 80.0 in nonfeeding dives.

Explain briefly without actually constructing the intervals.

(d)Which is wider:

(1)a 95% prediction interval for the mean oxygen consumption in a feeding dive of a single seal with a measure of 75.0 in nonfeeding dives.

(2)a 95% prediction interval for the mean oxygen consumption in a feeding dive of a single seal with a measure of 50.0 in nonfeeding dives.

Explain briefly without actually constructing the intervals. (In the data set, the mean oxygen consumption in nonfeeding dives was 74.68.)

(e)The coefficient of determination is 0.9345. Find a numerical value for the correlation coefficient. How do you know if it is positive or negative?

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