Question

5. (20 pts) Suppose that we have a dataset {(yi, x, Tt2, X;3), i,1,... ,n} together with some general belief on the data that higher (lower) value of each covariate x; (j = 1,2,3) will tend to result in higher (lower) y. In this study, we are interested in predicting y; from the total set of the regressors x;i, X;2, xt3. So, we apply the multiple linear regression yi = Bo+B1x1 +B2x52 + B3x43 + t to the data and some output results of the application are given: Coefficients: t value Pr(> |t|) Std Estimate Error Bo -0.06996 0.25064 -0.28 0.7810 B1 1.10126 1.41056 0.78 0.4378 B2 2.32206 1.48129 1.57 0.1218 BB -2.28100 2.22045 -1.03 0.3080 Residual standard error: 2.07026 on 66 degrees of freedom 0.1072 Multiple R-Squared: 0.2063, Adjusted R-squared: 5.72 on 3 and 66 DF, p-value: F-statistic 0.0015 Here, we assume that the usual assumptions can be made on e;. (a) (7 pts) Do you think if there exists a problem in the data for the above regression analysis? If so, identify a type of problem and explain why you think so. (b) (7 pts) Explain how to detect the problem answered in the above (a), using a numeric measure/statistic (c) (6 pts) State three alternative methods that might circumvent this problem an- swered in the (a). 1. 2. 3

Answer 1

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