Let sx and sy denote the sample standard deviations of the observed x’s and y’s, respect...

Let s_x and s_y denote the sample standard deviations of the observed x’s and y’s, respectively [that is S²_x = , and similarly forS²_y ].

a. Show that an alternative expression for the estimated regression line

b. This expression for the regression line can be interpreted as follows. Suppose r = .5. What then is the predicted y for an x that lies 1 SD (s_x units) above the mean of the x_i’s? If r were 1, the prediction would be for y to lie 1 SD above its mean . Using the data in Exercise 64 for a patient whose age is 1 SD below the average age in the sample, by how many standard deviations is the patient’s predicted ΔCBG above or below the average ΔCBG for the sample?

Reference exercise 64

The article “Increases in Steroid Binding Globulins Induced by Tamoxifen in Patients with Carcinoma of the Breast” (J. of Endocrinology, 1978: 219–226) reports data on the effects of the drug tamoxifen on change in the level of cortisol- binding globulin (CBG) of patients during treatment. With age= x and Δ CBG = y, summary values are n = 26,

a. Compute a 90% CI for the true correlation coefficient r.

b. Test H0: ρversus at level .05.

c. In a regression analysis of y on x, what proportion of variation in change of cortisol-binding globulin level could be explained by variation in patient age within the sample?

d. If you decide to perform a regression analysis with age as the dependent variable, what proportion of variation in age is explainable by variation in ΔCBG?