510 CHAPTER 9 Correlation and Regression SOLUTION Enter the y@values in C1 and the x1@, x2@, and x3@values in C2, C3, and C4, respectively. From the Stat menu, select “Regression▶Regression▶Fit Regression Model.” Using the salaries as the response variable and the remaining data as the continuous predictors, you should obtain results similar to the display shown. MINITAB Regression Analysis: Salary, y versus x1, x2, x3 Regression Equation Salary, y = 49764 + 364.4 x1 + 228 x2 + 267 x3 Coefficients Term Coef SE Coef T-Value P-Value Constant 49764 1981 25.12 0.000 x1 364.4 48.3 7.54 0.002 x2 228 124 1.84 0.140 x3 267 147 1.81 0.144 Model Summary S R-sq R-sq(adj) R-sq(pred) 659.490 94.38% 90.17% 48.98% b m1 m2 m3 The regression equation is ny = 49,764 + 364x 1 + 228x2 + 267x3. TRY IT YOURSELF 1 A statistics professor wants to determine how students’ final grades are related to the midterm exam grades and number of classes missed. The professor selects 10 students and obtains the data shown in the table. Student Final grade, y Midterm exam, x1 Classes missed, x2 1 81 75 1 2 90 80 0 3 86 91 2 4 76 80 3 5 51 62 6 6 75 90 4 7 44 60 7 8 81 82 2 9 94 88 0 10 93 96 1 Use technology to find a multiple regression equation that models the data. Answer: Page A42 Minitab displays much more than the regression equation and the coefficients of the independent variables. For instance, it also displays the standard error of estimate, denoted by S, and the coefficient of determination, denoted by R@Sq. In Example 1, S = 659.490 and R@Sq = 94.38%. So, the standard error of estimate is $659.49. The coefficient of determination tells you that 94.38% of the variation in y can be explained by the multiple regression model. The remaining 5.62% is unexplained and is due to other factors, such as sampling error, coincidence, or lurking variables. Study Tip In Example 1, it is important that you interpret the coefficients m1, m2, and m3 correctly. For instance, if x2 and x3 are held constant and x1 increases by 1, then y increases by $364. Similarly, if x1 and x3 are held constant and x2 increases by 1, then y increases by $228. If x1 and x2 are held constant and x3 increases by 1, then y increases by $267.
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