Do Problem 2.17.1 in the Weisberg (2014) text. With respect to Problem 2.17.2, simply compute bata1, but you can ignore the rest of it (Hint: Models are fit in R without the intercept by adding a -1 to the formula. Also, you do not need to do Problem 2.17.3.)

2.17 Regression through the origin Occasionally, a mean function in which the intercept is known a priori to be 0 may be fit. This mean function is given by E(yx) = Bix (2.27) The residual sum of squares for this model, assuming the errors are inde- pendent with common variance o', is RSS = E(M - Bix. ). 2.17.1 Show that the least squares estimate of B, is , = Exy/Xx/. Show that B, is unbiased and that Var (B,LX ) = o'/Ex, . Find an expres- sion for 6. How many of does it have? 48 CHAPTER 2 SIMPLE LINEAR REGRESSION 2.17.2 (Data file: snake) The data file gives X = water content of snow on April 1 and Y = water yield from April to July in inches in the Snake River watershed in Wyoming for n = 17 years from 1919 to 1935 (Wilm, 1950). Fit a regression through the origin and find S, and o'. Obtain a 95% confidence interval for B. Test the hypothesis that the slope , = 0.49, against the alternative that BI >0.49. 2.17.3 Plot the residuals versus the fitted values, and comment on the adequacy of the mean function with 0 intercept. In regression through the origin, Ze, #0