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A federal government agency that is responsible for setting vehicle fuel economy standards for automobile manufacturers is conducting research in order to update its fuel economy standards for the year 2030. Automobile manufacturers, and consumers, are highly interested in what the agency's findings and determinations will be as this will affect every vehicle in the United States. The federal government agency is very interested in the relationship between the weight of a vehicle and the vehicle's fuel economy (average miles per gallon (MPG)). Specifically, the agency is concerned that if the current trend of automobile manufacturers producing heavier new vehicles continues that its fuel economy targets will not be met. The agency's research department recently collected data for analysis in order to support the agency's upcoming discussion with the industry regarding its proposed 2030 fuel economy standards. The average MPG from a random sample of 750 vehicles was recently calculated by the agency. The research division also collected the vehicle weight of these 750 randomly sampled vehicles. The Vehicle Number, Type, Vehicle Weight, Average MPG, Fuel Tank Size (Gallons), Engine Size (Liters), and Meet or Not Meet Current Standards data were collected for these 750 vehicles1. Agency leadership wants to create a simple linear regression model to predict a vehicle's average fuel economy based on the weight of the vehicle.Create a scatterplot using Vehicle Weight as the independent variable and Average MPG as the dependent variable. Perform a visual analysis of the data: describe the trend, strength, and shape of the relationship between these two variables. Choose the correct answer below.A. The scatterplot indicates there is a positive, strong, linear relationship between Vehicle Weight and Average MPG.B. The scatterplot indicates there is a positive, weak, linear relationship between Vehicle Weight and Average MPG.C. The scatterplot indicates there is a negative, strong, linear relationship between Vehicle Weight and Average MPG D. The scatterplot indicates there is a negative, weak, linear relationship between Vehicle Weight and Average MPG.E.The scatterplot indicates there is no relationship between Vehicle Weight and Average MPG.1.1. Include the scatterplot image as part of your answer. Save the image as a .jpg or .png file, then click "Show Work" and use the "Insert Image" button to upload and save your scatterplot.1.2. Based upon your visual analysis of the scatterplot, is simple linear regression appropriate? Why or why not?2. What is the correlation coefficient between Vehicle Weight and Average MPG? (Round to two decimal places)2.1. Interpret the correlation coefficient in this context.3. Using your simple linear regression model, what is the value for the slope for this regression model? (Round to decimal places)3.1. Interpret the slope in this context.4. Using your simple linear regression model, what is the value for the y-intercept for this regression model? (Round to two decimal places)4.1. Interpret the y-intercept in this context.5. Using your simple linear regression model, for each one pound increase in vehicle weight, how much would one predict the vehicle's average fuel economy to decrease? (Round to three decimal places)5.1. Using your simple linear regression model, what is the predicted Average MPG of a vehicle when the Vehicle Weight is 2700 pounds (round the slope to 3 decimal places and y-intercept to 2 decimal places)?5.2. Based upon your simple linear regression, should the agency's leadership be concerned that if new vehicles continue to be produced with heavier weights that its goal of better fuel economy will be jeopardized?6. Another facet of the weight of the car is the question of whether or not weight differs for cars that meet standards and those that do not. Create a side-by-side boxplot of the weight of cars, distinguishing between cars that meet standards and those that do not.Include the side-by-side boxplot image as part of your answer. Save the image as a .jpg or .png file, then click "Show Work" and use the "Insert Image" button to upload and save your boxplot.6.1. Describe and interpret the shapes of the two boxplots.7. One typically expects that e.g. trucks have a different fuel efficiency than passenger cars. That could be tested by a two-sample t-test, but we do not have two types of cars, but more than two. Our two-sample test won't help to compare passenger cars, SUVs, and trucks. As such, conduct an ANOVA F-test to investigate if the average fuel efficiency of cars differs between the three types of cars.Now run the One Way ANOVA. What is the value of the test statistic of this ANOVA test?Test statistic = (Round to two decimal places)7.1. What are the degrees of freedom of the test statistic of the ANOVA test?Degrees of Freedom (Total)= (Type a whole number)7.2. What is the P-value of the test statistic of the ANOVA test?P-value= (Round to three decimal places)7.3. Describe in your own words what you conclude from the outcome of this ANOVA test. Is it in line with the expectations you had?8. One typically expects that e.g. trucks have a different fuel efficiency than passenger cars. That could be tested by a two-sample t-test, but we do not have two types of cars, but more than two. Our two-sample test won't help to compare passenger cars, SUVs, and trucks.If we wish to investigate if the average fuel efficiency of cars differs between the three types of cars, what type of analysis do we need?A.Two-sample t-testB.χ2 test for independenceC. ANOVA F-testD. χ2 test for homogeneity8.1. What is the null hypothesis of the test that there is no difference in fuel efficiency between the types of cars?A. All medians of fuel efficiency are equal for the three types of carsB. All means of fuel efficiency are equal for the three types of carsC. At least one means of fuel efficiency differs from the means of the other two types of carD. All three means of fuel efficiency are different for the three types of cars8.2. What is the alternative hypothesis of the test that there is no difference in fuel efficiency between the types of cars?A. All means of fuel efficiency are equal for the three types of carsB. All medians of fuel efficiency are equal for the three types of carsC. All three means of fuel efficiency are different for the three types of carsD. At least one means of fuel efficiency differs from the means of the other two types of cars8.3. Create side-by-side boxplots in StatCrunch. What type of car has the highest variability in fuel efficiency (judge by the graph, do not calculate)?A.TrucksB. Passenger carsC. SUVs8.4. And again looking at the side-by-side boxplot only, without yet doing any calculations: do you expect to find significant differences in mean fuel efficiency between the types of cars?A. No, because differences in medians are small.B. No, because differences in medians are small relative to the amount of variation within each type.C. Yes, because differences in medians are small relative to the amount of variation within each type.D. Yes, because differences in medians are small.