We want to test whether or not the addition of 3 variables to a model will be st

Question

We want to test whether or not the addition of 3 variables to a model will be statistically significant. You are given the following information based on a sample of 25 observations. Y-6242-1.836%, + 25.625, SSE-725 SSR-526 The equation was also estimated including the 3 variables. The results are Ye 59.23-1.762x, +25.638 16 237x3+15 297%-1872x5 SSE = 520 SSR = 731 Refer to Exhibit 16-6 The value of F- statistic (test statistic) for testing which model has significantly lower SSE is: F-2.497 F-3.6 F-4.55 F-1.775

Explanation / Answer

1)

TS = ((SSR_r - SSR_ur)/q) / (SSR_ur / (n-k-1))

Here

Q = 3 , k = 5, n = 25

SSR_r = 725

SSR_ur = 520

TS = ((725 – 520)/3 )/(520/(25-5-1)

= 2.4967

optionA) is correct

2)

TS = ((SSR_r - SSR_ur)/q) / (SSR_ur / (n-k-1))

Here

q = 1 , k = 3, n =   sample size = 28

SSR_r = 1425

SSR_ur = 1300

TS = ((1425-1300)/1 )/(1300/(n-3-1)

= (n-4)* 125/1300

= 0.096153* (n-4)

= 2.307672

df1 = q = 1 , df2 = n-k-1 = 24

critical value = 4.26 (from table)

option B) is correct

3)

df = n-k-1 = 25 -3-1 = 21

t-critical = 2.080

P(t < t*) = 0.975

option D) is correct

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