Lab 4a Miles per GallonIn the course website, open the Lab 4 mpg data and copy into Minitab. This data compares the miles per gallon of several cars against the speed the car was going as well as displacement (a measure reflecting engine weight).1) Do regression to predict mpg from speed and displacement {in MINITAB stat>>regr>>regression}. mpg=a + b*speed + c*displacement Look at residual vs. speed and residual vs. displacement plots. 1a) What is the regression equation and R2?1b) What do the two residual plots tell you? Create speed2, ln(speed), displacement2, and a speed * displacement terms in new columns. 2) Which of the following regression equations would create a better model for your data? Use the residual plot in question 1) to explain why.mpg = a +b*speed2+ c*displacement or mpg = a +b*ln(speed) + c*displacement 3) What is the regression equation and R2 if all 6 terms are included in the model?4) Give the regression equation and R2 value of the best model using some combination of all 6 terms. Note that including all 6 variables will give the highest R2 value. But some of the terms really have very little impact on R2. The idea is to find the simplest model (fewest variables) without significantly reducing the R2 value.5) Predict the mpg using the regression equations in 1) and 4). Speed Displacementpredicted for model 1) predicted for model 4) Actual1) residual 4)residual20.5 1.6480.3 3.1138 2.673 1.976) Use table 5) to compare the predicted values to the actual values. Why is Model 4) the best? Explain how you used R2 to find the best regression equation.7) Put all the data into stat>>regr>>stepwise in MINITAB, what model does it suggest to use?LAB 4b 2000 Presidential electionsOpen the Florida election data 2000pres and copy into Minitab.The 2000 presidential election is infamous for the close outcome and the confusing “butterfly ballot” which some voters claim led them to inadvertently select a candidate for whom they did not intend to vote (Pat Buchanan instead of Al Gore). Do not turn in graphs. Answer each question in two sentences or less.1) Look at the relationship between Bush, Buchanan, and Gore votes. (3 scatterplots)Use the brush command to identify which counties had unusual outcomes.2) Create a regression equation and R2 value to predict Buchanan from Bush. What are the residual values of Palm Beach, Dade, and Sarasota counties?Remove Palm Beach from the dataset and calculate the regression equation and R2.Now remove Dade from the dataset and calculate the regression equation and R2.Now remove Sarasota from the dataset and calculate the regression equation and R2.Identify any counties you consider to be influential and explain why.4) Plot Bush votes vs. # registered republicans, Gore vs. # registered democrats, and Buchanan vs. total registered reformed and independent voters. Find the regression line predicting number of Buchanan votes verse number of people registered in these parties. What are the residual values of Palm Beach, Dade, and Sarasota counties?5) See the following website for the chronology of the 2000 electionhttp://www.infoplease.com/ipa/A0884144.htmlDo the graphs and data produced above show evidence of ballot problems? Why or why