SECTION 9.4 Multiple Regression 511 Predicting y-Values After finding the equation of the multiple regression line, you can use the equation to predict y@values over the range of the data. To predict y@values, substitute the given value for each independent variable into the equation, then calculate ny. Predicting y-Values Using Multiple Regression Equations Use the regression equation ny = 49,764 + 364x 1 + 228x2 + 267x3 found in Example 1 to predict an employee’s salary for each set of conditions. 1. 12 years of current employment 5 years of previous experience 16 years of education 2. 4 years of current employment 2 years of previous experience 12 years of education 3. 8 years of current employment 7 years of previous experience 17 years of education SOLUTION To predict each employee’s salary, substitute the values for x1, x2, and x3 into the regression equation. Then calculate ny. 1. ny = 49,764 + 364x 1 + 228x2 + 267x3 = 49,764 + 3641122 + 228152 + 2671162 = 59,544 The employee’s predicted salary is $59,544. 2. ny = 49,764 + 364x 1 + 228x2 + 267x3 = 49,764 + 364142 + 228122 + 2671122 = 54,880 The employee’s predicted salary is $54,880. 3. ny = 49,764 + 364x 1 + 228x2 + 267x3 = 49,764 + 364182 + 228172 + 2671172 = 58,811 The employee’s predicted salary is $58,811. TRY IT YOURSELF 2 Use the regression equation found in Try It Yourself 1 to predict a student’s final grade for each set of conditions. 1. A student has a midterm exam score of 89 and misses 1 class. 2. A student has a midterm exam score of 78 and misses 3 classes. 3. A student has a midterm exam score of 83 and misses 2 classes. Answer: Page A42 EXAMPLE 2 Picturing the World In a lake in Finland, 159 fish of 7 species were caught and measured for weight G (in grams), length L (in centimeters), height H, and width W (H and W are percents of L). The regression equation for G and L is G = -491 + 28.5L, r ≈ 0.925, r 2 ≈ 0.855. When all four variables are used, the regression equation is G = -712 + 28.3L + 1.46H + 13.3W, r ≈ 0.930, r 2 ≈ 0.865. (Source: Journal of Statistics Education) Predict the weight of a fish with the following measurements: L = 40, H = 17, and W= 11. How do your predictions vary when you use a single variable versus many variables? Which do you think is more accurate?
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