(Use R for data analysis) An experiment was conducted to evaluate the effect of vitamin C on tooth growth. Sixty guinea pigs received various doses of vitamin C by one of two delivery methods, orange juice or ascorbic acid. Results of this experiment are in dataset ''ToothGrowth'' which is already loaded in R. You can look at it with commands attach(ToothGrowth), names(ToothGrowth), summary(ToothGrowth), ToothGrowth.

The data set contains the following variables: len: Tooth length supp: supplement or delivery method (OJ = orange juice, VC = ascorbic acid) dose: Dose in milligrams/day

(a) Fit a linear regression model that can be used to predict the tooth length based on the dose and the delivery method of vitamin C.

(b) Is delivery method significant?

(c) Is there a significant interaction between the dose and the delivery method, at = 5% level?

(d) Write two regression equations explicitly, one equation for each delivery method.

(e) What percent of the total variation of the tooth length is explained by this regression?