Please solve this problem using R-commands and their output (please show your R-codes):

Exercise 5.3 (using data Example 4.12): Test the homogeneity of variance using LeveneTest, fit a regression model and

1. determine if there is a difference in the mean of the 3 groups (1,2, and 3).

2. determine which group has the largest mean.

Example 4.12 (Fuel Additive) Three different additives that are marketed for increas- ing fuel efficiency in miles per gallon (mpg) were evaluated by a testing agency. Studies have shown an average increase of 8% in mpg after using the products for 250 miles. The testing agency wants to evaluate the variability in the increase. (We will see in later sections how to compare the means). Additive % in mpg Additive % f in mpg Additive % 1 in mpg 1 4.2 2 0.2 3 7.2 1 2.9 2 11.3 6.4 1 0.2 2 0.3 9.9 1 25.7 2 17.1 3.5 1 6.3 2 51.0 10.6 1 2 10.1 10.8 1 2.3 2 0.3 10.6 1 9.9 2 0.6 8.4 1 5.3 2 7.9 6.0 1 6.5 2 7.2 11.9 7.2 Example 4.12 (Fuel Additive) Three different additives that are marketed for increas- ing fuel efficiency in miles per gallon (mpg) were evaluated by a testing agency. Studies have shown an average increase of 8% in mpg after using the products for 250 miles. The testing agency wants to evaluate the variability in the increase. (We will see in later sections how to compare the means). Additive % in mpg Additive % f in mpg Additive % 1 in mpg 1 4.2 2 0.2 3 7.2 1 2.9 2 11.3 6.4 1 0.2 2 0.3 9.9 1 25.7 2 17.1 3.5 1 6.3 2 51.0 10.6 1 2 10.1 10.8 1 2.3 2 0.3 10.6 1 9.9 2 0.6 8.4 1 5.3 2 7.9 6.0 1 6.5 2 7.2 11.9 7.2