SECTION 9.4 Multiple Regression 513 Using and Interpreting Concepts Finding a Multiple Regression Equation In Exercises 7 and 8, use technology to find (a) the multiple regression equation for the data shown in the table, (b) the standard error of estimate, and (c) the coefficient of determination. Interpret the results. 7. Used Cars The table shows the prices (in dollars), age (in years), and mileage (in thousands of miles) of nine pre-owned Honda Civic sedans. Price, y Age, x1 Mileage, x2 $20,368 2 11.0 $16,889 3 83.7 $11,300 5 83.0 $19,430 3 27.0 $9777 7 94.9 $9899 6 88.0 $14,600 6 27.8 $19,930 4 23.1 $19,000 5 46.5 8. Nutrition The table shows the calories, fat (in grams), carbohydrates (in grams), and protein (in grams) per serving size of eight common foods. Food Calories, y Fat (g), x1 Carbs (g), x2 Protein (g), x3 Eggs 80 5 0 7 Broccoli 31 0 6 3 Potato chips 160 10 15 2 Sirloin steak 240 16 0 22 Avocado 240 22 13 3 Shredded cheddar 110 9 2 7 Snickers bar 250 12 32 4 Wheat bread 70 1 13 3 Extending Concepts Adjusted r 2 The calculation of the coefficient of determination r2 depends on the number of data pairs and the number of independent variables. An adjusted value of r2 based on the number of degrees of freedom is calculated using the formula r2 adj = 1 - c 11 - r221n - 12 n - k - 1 d where n is the number of data pairs and k is the number of independent variables. In Exercises 9 and 10, calculate r2 adj and determine the percentage of the variation in y that can be explained by the relationships between variables according to r2 adj. Compare this result with the one obtained using r2. 9. Calculate r2 adj for the data in Exercise 7. 10. Calculate r2 adj for the data in Exercise 8.
RkJQdWJsaXNoZXIy NjM5ODQ=