A sample of 20 automobiles was taken, and the miles per gallon (MPG), horsepower

Question

A sample of 20 automobiles was taken, and the miles per gallon (MPG), horsepower, and total weight were MPG HORSEPOWER WEIGHT (xa) 67 1.844 50 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 35 32 30 28 20 21 18 18 153 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 (r)) (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) INSTRUCTIONS .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) y=53,87-0.2694x1 and y=57.53-10.7864x2

using ms-excel the regression analysis showed that model with x1(horsepower) is better as its r2=0.7702 is more than model with x2(weight) whose r2=0.7326. both the model is significant

(b) y=57.69-0.1657x1-0.5046x2

in this case r2=0.8126 and overall model is significant. here x1 is significant but x2 is not

(c) y=69.93-0.62x1+0.0017x1*x1

Regression Statistics Multiple R 0.877606954 R Square 0.770193965 Adjusted R Square 0.757426963 Standard Error 4.481278353 Observations 20 ANOVA df SS MS F Significance F Regression 1 1211.476598 1211.477 60.32692 3.72351E-07 Residual 18 361.4734022 20.08186 Total 19 1572.95 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 53.87237626 3.423059926 15.73808 5.76E-12 46.68079422 61.06395829 x1 -0.269447549 0.034691146 -7.76704 3.72E-07 -0.342330942 -0.196564156

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.