3. The file w logret 3automanu.txt contains the weekly log returns of three auto manufacturers, General Motors Corp., Ford Motor Corp., and Toyota Motor Corp., from the week of January 3, 1994 to the week of June 25, 2007. Consider the regression model GM = ?0 + ?1Toyota + ?2Ford + .

Write R code to solve the following.

(a) Estimate ?0, ?1 and ?2 by least squares and give their 95% confidence intervals.

(Note the confidence intervals can be obtained by confint(fit,level=0.95), where fit is the fitted model from lm().)

(b) Test the null hypothesis H0 : ?1 = 0 vs HA : ?1 6= 0 and give the pvalue.

(c) Perform regression diagnostics of the fitted regression model by relevant plots and statistics. Conclusions must be based on patterns observed in the plots or values of the statistics.

(d) Identify high leverage observations based on Cook's distance, if there are any.

3. The file w_logret_3automanu. txt contains the weekly log returns of three auto man- ufacturers, General Motors Corp., Ford Motor Corp., and Toyota Motor Corp., from the week of January 3, 1994 to the week of June 25, 2007. Consider the regression model GM = Bo + BiToyota + 32 Ford + E. Write R code to solve the following. (a) Estimate Bo, B1 and 32 by least squares and give their 95% confidence intervals. (Note the confidence intervals can be obtained by confint (fit, level=0.95), where fit is the fitted model from Im ().) (b) Test the null hypothesis Ho : B1 = 0 vs HA : B1 + 0 and give the pvalue. (c) Perform regression diagnostics of the fitted regression model by relevant plots and statistics. Conclusions must be based on patterns observed in the plots or values of the statistics. (d) Identify high leverage observations based on Cook's distance, if there are any