Let sx and sy denote the sample standard deviations of the observed x's and y's, respectively [that is, s2x = ((xi - xÌ…)2 / (n - 1) and similarly for s2y].
a. Show that an alternative expression for the estimated regression line y = 0 + 1x is

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 (sx units) above the mean of the xi's? If r were 1, the prediction would be for y to lie 1 SD above its mean y, but since r = .5, we predict a yÌ… that is only .5 SD (.5sy unit) above y. Using the data in Exercise 64, when UV transparency index is 1 SD below the average in the sample, by how many standard deviations is the predicted maximum prevalence above or below its average for the sample?

Transcribed Image Text:

y = y +r. 2(x – x) – x)