Please answer the following question with the help of R Studio.

Q2. Table 1 summarizes the results of a linear regression model using a subset of the "mtcars" data. The goal is to analyze fuel efficiency (mpg) using two independent variables "wt" (weight) and "cyl" (number of cylinders). The "cyl" is a categorical variable with three levels: "4", "6" and "8" and can be recoded using two dummy variables D2 and D3. mpg = Bo + B,*wt + B2*D2 + B,*D3 + , u is IID N(0, o') mpg : miles per gallon wt : weight (measured in 1000 lbs) D2 : the number of cylinders is six (D2 = 1 when cyl = 6, D2 = 0 when cyl # 6) D3 : the number of cylinders is eight (D3 = 1 when cyl = 8, D3 = 0 when cyl # 8) Table 1 Coefficients: Estimate Std. Error t value Pr(> |t[) (Intercept) 33.6445 2.1116 15.933 1.33e-14 *#* wt -3.1258 0.8219 3.803 0.00082 *** cyl (= 6) -4.1918 1.6093 [ A ] B cyl (= 8) -6.0436 1.7505 -3.452 0.00199 **Signif. codes: ( **0.001 * 0.01 0.05 0.1 "1 Residual standard error: 2.682 on 25 degrees of freedom Multiple R-squared: 0.8227, Adjusted R-squared: [ C ] F-statistic: [ D ], p-value: [ E ] a) Please fill in cell A, B, C, D, and E. Present your computational process in details; you also need to provide the corresponding R codes for both cell B and E b) What is the respective meaning of the estimated coefficients "-4.19" and "-6.04" for both dummy variables D2 and D3? c) What is the purpose of the F statistic (i.e., cell D) presented at the bottom of the table? Based on the corresponding p-value (i.e., cell E), what can you conclude? d) What is the predicted mpg for a 4-cylinder car with 2 units (2000 lbs) of weight? Present the computation process and the predicted mpg. e) Suppose the ordering of the "cyl" is rearranged in the linear regression model as shown in Table 2, please fill in cell F, G and H and show you how to get these numerical values? Table 2 Estimate mpg = Bo + Bi*wt + 2*D2 + B*D3 + (Intercept) IF D2: the number of cylinders is four wt -3.1258 D3: the number of cylinders is eight CYL( = 4) G CYL( = 8) H What are new estimated Bo, B2, and By