Q 2 Pg 40 Stock Chapter 7: Hypothesis Testing/Confidence Intervals - Multiple regression

[Dr. Jayanthi Sankaran]

Hi David,

I am having problems in computing the F statistic for the above:

2. Following is an estimated regression, with includes standard errors:

Price (caret) = 119.2 + 0.485 BDR + 23.4 Bath + 0.156 Hsize + 0.002 Lsize - 0.090Age - 48.8 Poor
(23.9) (2.61) (8.94) (0.011) (0.00048) (0.311) (10.5)


R square = 0.72, SER = 41.5

Note that the above regression has six regressors. The F-statistic for omitting BDR and Age from the regression is 3.31. The following four critical values are provided to you: critical F(2df, infinite @5%) = 3.00; F(2df, infinite @1%) = 4.61; F(6df, infinite@5%) = 2.01, F(6df,infinite@1%) = 2.64. Are the coefficients BDR and Age statistically different from zero, at respectively, the 5% and 1% level?

My answer is:

SER = SQRT((SSRunrestricted)/(n - k - 1))
SER^2 = SSRunrestricted/(n - k - 1)
41.5^2 * (213) =SSRunrestricted = 366,839.25

SER^2 = SSRrestricted/217
41.5^2 = SSRrestricted/217
SSRrestricted = 41.5^2 * 217 = 373,728.25

Using the forumula for the F statistic

F = (SSRrestricted - SSRunrestricted)/q

SSRunrestricted /n - kunrestricted - 1)

= (373,728.25 - 366,839.25)/1.0 = 4.00

366,839.25/213​

Your answer for the F statistic is 3.31. Can you please explain how you get this number?

However, I must add that my calculated figure of 4.0 leads to the same conclusion as yours:

Although the regression has six regressors, we are restricting only two such that the correct critical values are F(2df, infinite)

• As computed F-statistic of 4.00 is GREATER THAN critical F(2df, infinite)@5% = 3.00; we reject the null; that is they are significant with 95% confidence
• As computed F-statistic of 4.00 is LESS than F(2df, infinite)@1% = 4.61, we fail to reject null; ie they are not significant with 99% confidence.

Thanks!
Jayanthi

 

[ShaktiRathore]

jayanti conclusions can be cross checked using tstatistic
Tstat(BDR)=0.485-0/2.61=.1858 is nowhere near sweetspot of 3 so we cant reject null and conclude BD is not statistically different from 0.
tstat(Age)=-.09-0/.311=.289<<3 suggests Age is also not statisticalky different from 0.

Also does the SER for restricted case shall remain the same as unrestricted case?,u have taken SER same for both cases as 41.5.
Thanks

 

[Dr. Jayanthi Sankaran]

Hi Shakti,

According to your t-statistic calculations, both BD and Age are not statistically different from zero. This is not the answer - if you look at David's and my answers (which reinforces David's) -

Although the regression has six regressors, we are restricting only two such that the correct critical values are F(2df, infinite)

• As computed F-statistic of 4.00 is GREATER THAN critical F(2df, infinite)@5% = 3.00; we reject the null; that is they are significant with 95% confidence
• As computed F-statistic of 4.00 is LESS than F(2df, infinite)@1% = 4.61, we fail to reject null; ie they are not significant with 99% confidence.

Also, only one SER of 41.5 is given in the data!

Thanks!
Jayanthi