sts 7Week 7 multiple_linear_regression

sts 7Week 7 multiple_linear_regression - Regression...

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Regression Analysis using X1, X2 and X3 R² 0.905 Adjusted R² 0.858 n 10 R 0.951 k 3 Std. Error 2.035 Dep. Var. Y ANOVA table Source SS df MS F p-value Regression 237.5416 3 79.1805 19.11 .0018 Residual 24.8584 6 4.1431 Total 262.4000 9 Regression output confidence interval variables coefficients std. error t (df=6) p-value 95% lower 95% upper Intercept 5.6567 2.8342 1.996 .0930 -1.2783 12.5918 X1 0.1939 0.0877 2.211 .0691 -0.0207 0.4085 X2 2.3381 0.9078 2.576 .0420 0.1168 4.5594 X3 -0.1628 0.2441 -0.667 .5296 -0.7600 0.4345 Regression Analysis using X1 and X2 R² 0.898 Adjusted R² 0.869 n 10 R 0.948 k 2 Std. Error 1.953 Dep. Var. Y ANOVA table Source SS df MS F p-value Regression 235.6989 2 117.8495 30.90 .0003 Residual 26.7011 7 3.8144 Total 262.4000 9 Regression output confidence interval variables coefficients std. error t (df=7) p-value 95% lower 95% upper Intercept 5.0911 2.5948 1.962 .0906 -1.0448 11.2269 X1 0.1649 0.0731 2.257 .0586 -0.0079 0.3376 X2 2.6569 0.7405 3.588 .0089 0.9060 4.4079 Predicted values for: Y 95% Confidence Interval 95% Prediction Interval X1 X2 Predicted lower upper lower upper Leverage 55 4 24.786 23.182 26.389 19.897 29.674 0.121
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Y X1 X2 X3 Variables 16 32 2 4 Y = Home Square Footage (Hundreds of Square Feet) 17 36 2 8 X1 = annual income (thousands of dollars) 26 55 3 7 X2 = Family Size 24 47 4 0 X3 = combined years of formal education (beyond high school) for 22 38 4 2 all household wage earners. 21 60 3 10 32 66 6 8 Note: Y is the dependent variable 18 44 3 8 X1, X2 and X3 are independent variables 30 70 5 2 20 50 3 6 Questions Solutions Examing this equation shows that Income (X1) and family size (X2) both positively affect house size, since their coefficients are positive. (This means the higher the income the larger the house and the larger the family the larger the house.) But, we see that Years of Formal Education (X3) has a negative affect on house size… Sometimes, strange things happen, like this negative education effect. These things are often explained by "multicollinearity"
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This note was uploaded on 10/08/2011 for the course STATISTIC GM533 taught by Professor Henry during the Spring '10 term at Keller Graduate School of Management.

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sts 7Week 7 multiple_linear_regression - Regression...

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