Type I and Type III Sums of Squares

[Pages:4]Type I and Type III Sums of Squares

Supplement to Section 8.3

Brian Habing ? University of South Carolina Last Updated: February 4, 2003

PROC REG, PROC GLM, and PROC INSIGHT all calculate three types of F tests: ? The omnibus test: The omnibus test is the test that is found in the ANOVA table. Its F statistic is found by dividing the Sum of Squares for the Model (the SSR in the case of regression) by the SSE. It is called the Test for the Model by the text and is discussed on pages 355-356. ? The Type III Tests: The Type III tests are the ones that the text calls the Tests for Individual Coefficients and describes on page 357. The p-values and F statistics for these tests are found in the box labeled Type III Sum of Squares on the output. ? The Type I Tests: The Type I tests are also called the Sequential Tests. They are discussed briefly on page 372-374.

The following code uses PROC GLM to analyze the data in Table 8.2 (pg. 346-347) and to produce the output discussed on pages 353-358. Notice that even though there are 59 observations in the data set, seven of them have missing values so there are only 52 observations used for the multiple regression.

DATA fw08x02;

INPUT Obs age bed bath

size

lot

price;

CARDS;

1

21

3

3.0 0.951

64.904

30.000

2

21

3

2.0 1.036 217.800

39.900

3

7

1

1.0 0.676

54.450

46.500

F

5

65695.79292

13139.15858

42.93

F

1

526.13923

526.13923

1.72

0.1965 B

1

10713.09272

10713.09272

35.00

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