7. Residual analysis Aa Aa Consider a multiple regression model of the dependent

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7. Residual analysis Aa Aa Consider a multiple regression model of the dependent variable y on independent variables x 1, x2, and x3: Using data with 12 observations for each of the variables, a researcher obtains the following estimated regression equation for the above model: 0.5216 1.2419x 1 0.3049x2 0.0217x3 The standard error of estimate for this equation is s 0.6489 The table below gives the values for the independent and dependent variables and their corresponding predicted values, residuals, and leverage. Predicted Value Residual Leverage (y) (y y) (h) No. X1 X2 X3 7.9611 15.0243 0.6987 15.9368 15.0042 0.9326 0.4520 0986 1.3892 0.8676 1.1405 1.4814 0.3408 0.1435 0.0988 5.4086 3.9838 0.3419 7.7636 7.4175 0.3461 0.4070 3.1600 1.1120 1.1186 0.9553 0.1632 0.2440 1.3257 4.3239 0.3301 0.2630 0.1862. 0.0768 0.0738 7.6853 11.5261 0.1471 12.3110 3.5768 1.2659 0.2514 1.3240 1.7893 10.0129 1.2846 1.3775 0.0536 0.4710 0.5359 3.5670 0.3263 1.3994 0.9364 0.4631 0.0440 0.2575 7.6694 8849 -0.2815 9.7355 9.4779 0.3518 12.7237 10 8.6307 4.8937 0.3933 12.5416 0.1821 0.3679 11 4.8492 6.7252 0.0790 7.8382 7.5493 0.2890 0.0936 12 0189 10.2205 0.744 3.3985 3.8757 0.4771 0.4082 Use information from the table to answer the following questions. The standard deviation of the residual for the tenth observation y10 12.5416 is The standardized 0.3679 residual for the tenth observation is 0.3996 0.0500 0.5159

Explanation / Answer

Under the null hypothesis that the tenth observation is not an outlier, its studentized deleted residual follows t-distribtuion with 7 degrees of freedom. At significance level 0.01, the critical values for the test of the null hypothesis using the studentized deleted residual are -3.499 to 3.499. Thus, you can not conclude that the tenth observation is an outlier.

When an observation is an outlier, it is easier to detect it with the studentized deleted residual than with the standardized residual

The rule of thumb indicates that there are no influential observations in the data presented above.

Cook's distance measure uses both the leverage and the residual of an observation to determine whether the observation is influential

Cook's distance for the second observation is o.1010. using the rule of thumb given in your textbook, this does not indicate that the observation is influential

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