This exercise uses the data given seed weight of soybeans Y to cumulative seasonal solar radiation X for two levels of ozone exposure. For simplicity in plotting, rescale X by dividing by 2 and Y by...

This exercise uses the data given seed weight of soybeans Y to cumulative seasonal solar radiation X for two levels of ozone exposure. For simplicity in plotting, rescale X by dividing by 2 and Y by dividing by 100 for this exercise.

(a) Use the “Low Ozone” data to compute the linear regression of Y on X (with an intercept). Compute
 and e, the lengths of all vectors, and the angle between each pair of vectors. Use the vector lengths and angles to display graphically the regression results. Use your figure to “estimate” the regression coefficients. From the relative positions of the vectors, what is your judgment as to whether the intercept is needed in the model?

(b) Repeat Part (a) using the “High Ozone” data.

(c) Compare the graphical representations of the two regressions. What is your judgment as to whether the regressions are homogeneous—that is, are the same basic relationships—within the limits of random error, illustrated in both figures.