Use the data and regression equation from Exercise 1.4 and compute Yi for each value of X. Compute the product moment correlations between Compare these correlations to each other and to the...

Use the data and regression equation from Exercise 1.4 and compute Yi for each value of X. Compute the product moment correlations between

Compare these correlations to each other and to the coefficient of determination R2. Can you prove algebraically the relationships you detect?

Exercise 1.4

The data in the accompanying table relate heart rate at rest Y to kilograms body weight X.

(a) Graph these data. Does it appear that there is a linear relationship between body weight and heart rate at rest?

(b) Compute

₀
and

₁
and write the regression equation for these data. Plot the regression line on the graph from Part (a). Interpret the estimated regression coefficients.

(c) Now examine the data point (67, 40). If this data point were removed from the data set, what changes would occur in the estimates of β₀
and β₁?

(d) Obtain the point estimate of the mean of Y when X = 88. Obtain a 95% confidence interval estimate of the mean of Y when X = 88. Interpret this interval statement.

(e) Predict the heart rate for a particular subject weighing 88kg using both a point prediction and a 95% confidence interval. Compare these predictions to the estimates computed in Part (d).

(f) Without doing the computations, for which measured X would the corresponding
 have the smallest variance? Why?