Question: 1. We develop an MLR model for estimating heating oil usage (Y ) used for a single-family home based on average temperature temp (X1 )

1. We develop an MLR model for estimating heating oil usage (Y ) used for a single-family home based on average temperature temp (X1 ) and amount of insulation (X2 ) in inches. We fit the model with 16 cases and list their case statistics:

1. We develop an MLR model for estimating heating

(a) Explain the means of the case statistics in the first three rows (DFBETAS1, DFBETAS2, and DFFITS).

(b) R identifies two cases whose values indicate possible outliers: #8 and #16. For #8, is it unusual w.r.t to its values of predictors or response variable? Why?

(d) Which case should we remove as a true outlier?

2. Among the case statistic leverage hi, which of the following statement is not true?

a) hi is calculated using explanatory variables X only.

b) The observation with a large hi must be an outlier.

c) hi is the i^th diagonal element of the hat matrix H .

d) None of above.

DFBETAS1 DFBETAS2 DFFITS CookDis Leverage 1 0.02156 -0.121033 0.1641 0.009590 0.1379 2 -0.09621 -0.226361 0.3382 0.039150 0.1474 3 -0.00176 0.036339 0.0454 0.000744 0.1750 4 -0.16825 0.022263 -0.1956 0.013678 0.2407 5 -0.04730 0.006680 -0.0606 0.001323 0.1604 6 -0.00435 -0.000434 0.0214 0.000165 0.0653 7 -0.19820 0.015194 0.2423 0.020762 0.1893 8 -0.13747 0.127702 0.1975 0.013998 0.3390 * 9 -0.04909 0.078606 0.1043 0.003918 0.2245 10 -0.09643 0.089201 -0.1449 0.007537 0.2433 11 -0.09839 -0.103441 -0.1736 0.010802 0.2575 12 0.00249 -0.001077 0.0190 0.000131 0.0637 13 -0.29041 -0.397278 0.6548 0.131650 0.1687 14 0.02153 -0.238592 0.3245 0.036015 0.1361 15 -0.07844 -0.120630 -0.1799 0.011573 0.2158 16 5.19406 3.862653 -7.9761 1.260195 0.2353 * DFBETAS1 DFBETAS2 DFFITS CookDis Leverage 1 0.02156 -0.121033 0.1641 0.009590 0.1379 2 -0.09621 -0.226361 0.3382 0.039150 0.1474 3 -0.00176 0.036339 0.0454 0.000744 0.1750 4 -0.16825 0.022263 -0.1956 0.013678 0.2407 5 -0.04730 0.006680 -0.0606 0.001323 0.1604 6 -0.00435 -0.000434 0.0214 0.000165 0.0653 7 -0.19820 0.015194 0.2423 0.020762 0.1893 8 -0.13747 0.127702 0.1975 0.013998 0.3390 * 9 -0.04909 0.078606 0.1043 0.003918 0.2245 10 -0.09643 0.089201 -0.1449 0.007537 0.2433 11 -0.09839 -0.103441 -0.1736 0.010802 0.2575 12 0.00249 -0.001077 0.0190 0.000131 0.0637 13 -0.29041 -0.397278 0.6548 0.131650 0.1687 14 0.02153 -0.238592 0.3245 0.036015 0.1361 15 -0.07844 -0.120630 -0.1799 0.011573 0.2158 16 5.19406 3.862653 -7.9761 1.260195 0.2353 *

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