Regression exercise using R math homework help

The datafile Tooth.docx contains measurements of the length of teeth in guinea pigs given different dose levels of Vitamin C (0.5, 1 and 2 mg) using two delivery methods (orange juice (OJ) or ascorbic acid (VC)) from birth. Experimenters were interested in whether the method of delivery, as well as the dose, effects teeth growth. (a) Assuming that the effect of dose is linear for each delivery method, use dummy variables to test whether there are differences between the regression lines for the two delivery methods. What can you conclude about the effect of Vitamin C if admininstered using orange juice or ascorbic acid? (b) Is the linearity assumption appropriate for each delivery method with these data?

You should answer by constructing a suitable linear model, carefully analysing the data using it and drawing suitable conclusions. Your answer should include diagnostic checks (such as analysis of residuals, identication of influential observations, etc.). You should use R. All computer output should be included in the text of your answer and commented upon.