A sample of 20 automobiles was taken, and the miles per gallon (MPG), horsepower
ID: 3065415 • Letter: A
Question
A sample of 20 automobiles was taken, and the miles per gallon (MPG), horsepower, and total weight were MPG HORSEPOWER WEIGHT 67 1.844 0 1.998 62 1.752 1.98 66 1.797 63 2.199 90 2.404 99 2.611 63 3.236 91 2.606 2.58 88 2.507 124 2.922 97 2.434 114 3.248 102 2.812 114 3.382 142 3.197 4.38 139 4.036 37 37 34 32 30 28 26 26 25 20 21 18 18 16 a. Develop a linear regression model to predict MPG, using horsepower as the only independent variable. Develop another model with weight as the independent variable. Which of these two models is better? Explain (Compare significances of the models and coefficient of determinations ))(40 points) Develop a multiple regression model that includes both horsepower and weight as the independent variables. Discuss significance of the model and coefficient of determination (r). (20 points) Develop a quadratic model as: b. c. Discuss significance of the model and coefficient of determination (r). (40 points) .Submit softcopy excel files via moodle Data file is attached as a separate xls file Models should be developed with MS Excel Data Analysis Tool as shown in the class. Every solution (regression model) should be on a different sheet. Discussion is to be made on the same sheet.Explanation / Answer
a: When the mpg is predicted from horsepower it gives r2 =0.77 indicating that horsepower predicts mpg 77% correctly. On the other side when we predict mpg from the weight it gives r2=0.14 indicating that the weight predicts mpg only 14%correctly.Thus we can say predicting mpg from horsepower is better than predicting it from the weight.
b: when both horsepower and the weight are used as independent variables it gives a value 0.77 of adjusted r2 ,which is quite satisfying but at the same time, the null hypothesis corresponding to weight gets accepted indicating that weight can be excluded from the model.
Hope this helps.Thank You