Figure:
Suppose that in the course of testing whether salary functions differ for males and females,you estimate the pooled and male and female results in Figure 6.4. $\text { Pooled }$

$\begin{array}{l}
\text { ANOVA }\
\begin{array}{lccccc}
\hline & d f & S S & M S & F & \text { Significance } F \
\hline \text { Regression } & 4 & 2.30931 \mathrm{E}+12 & 5.77328 \mathrm{E}+11 & 282.1787278 & 1.2198 \mathrm{E}-215 \
\text { Residual } & 4286 & 8.76901 \mathrm{E}+12 & 2045965635 & & \
\text { Total } & 4290 & 1.10783 \mathrm{E}+13 & & & \
\hline
\end{array}
\end{array}$

$\text { Male }$

$\begin{array}{l}
\text { ANOVA }\
\begin{array}{lccccc}
\hline & d f & S S & M S & F & \text { Significance } F \
\hline \text { Regression } & 4 & 1.54309 \mathrm{E}+12 & 3.85772 \mathrm{E}+11 & 131.8489492 & 9.4649 \mathrm{E}-101 \
\text { Residual } & 2136 & 6.24964 \mathrm{E}+12 & 2925860190 & & \
\text { Total } & 2140 & 7.79272 \mathrm{E}+12 & & & \
\hline
\end{array}
\end{array}$

$\text { Female }$

$\begin{array}{lccccc}
\text { ANOVA }\
\hline& \text { of } & S S & M S & F & \text { Significance } F \
\hline \text { Regression } & 4 & 6.15055 \mathrm{E}+11 & 1.53764 \mathrm{E}+11 & 153.1758618 & 2.2255 \mathrm{E}-115 \
\text { Residual } & 2145 & 2.15323 \mathrm{E}+12 & 1003838471 & & \
\text { Total } & 2149 & 2.76829 \mathrm{E}+12 & & &\
\hline
\end{array}$
Figure 6.4
-The tests statistic for the Chow test in Figure 6.4 is
A)0.0436.
B)9.327.
C)18.654.
D)37.307.

Question

Figure:
Suppose that in the course of testing whether salary functions differ for males and females,you estimate the pooled and male and female results in Figure 6.4. $\text { Pooled }$

$\begin{array}{l}
\text { ANOVA }\
\begin{array}{lccccc}
\hline & d f & S S & M S & F & \text { Significance } F \
\hline \text { Regression } & 4 & 2.30931 \mathrm{E}+12 & 5.77328 \mathrm{E}+11 & 282.1787278 & 1.2198 \mathrm{E}-215 \
\text { Residual } & 4286 & 8.76901 \mathrm{E}+12 & 2045965635 & & \
\text { Total } & 4290 & 1.10783 \mathrm{E}+13 & & & \
\hline
\end{array}
\end{array}$

$\text { Male }$

$\begin{array}{l}
\text { ANOVA }\
\begin{array}{lccccc}
\hline & d f & S S & M S & F & \text { Significance } F \
\hline \text { Regression } & 4 & 1.54309 \mathrm{E}+12 & 3.85772 \mathrm{E}+11 & 131.8489492 & 9.4649 \mathrm{E}-101 \
\text { Residual } & 2136 & 6.24964 \mathrm{E}+12 & 2925860190 & & \
\text { Total } & 2140 & 7.79272 \mathrm{E}+12 & & & \
\hline
\end{array}
\end{array}$

$\text { Female }$

$\begin{array}{lccccc} 
\text { ANOVA }\
\hline& \text { of } & S S & M S & F & \text { Significance } F \
\hline \text { Regression } & 4 & 6.15055 \mathrm{E}+11 & 1.53764 \mathrm{E}+11 & 153.1758618 & 2.2255 \mathrm{E}-115 \
\text { Residual } & 2145 & 2.15323 \mathrm{E}+12 & 1003838471 & & \
\text { Total } & 2149 & 2.76829 \mathrm{E}+12 & & &\
\hline
\end{array}$
Figure 6.4
-The tests statistic for the Chow test in Figure 6.4 is
A)0.0436.
B)9.327.
C)18.654.
D)37.307.

Quizplus · Accepted Answer

The Chow test is used to determine whether there is a structural break in the regression. In this case, we are comparing the pooled results to the male and female results to see if there is a significant difference between the two groups. The test statistic for the Chow test is calculated as follows:

$$F = \frac{(SS_{P} - SS_{M} - SS_{F})/(k_{M}+k_{F})}{(SS_{M} + SS_{F})/(n_{M}+n_{F}-2k_{M}-2k_{F})}$$

where $SS_{P}$, $SS_{M}$, and $SS_{F}$ are the sums of squares for the pooled, male, and female regressions, respectively; $k_{M}$ and $k_{F}$ are the number of variables in the male and female regressions; and $n_{M}$ and $n_{F}$ are the sample sizes for the male and female regressions.

Plugging in the values from the ANOVA tables, we get:

$$F = \frac{(1.10783 \mathrm{E}+13 - 7.79272 \mathrm{E}+12 - 2.76829 \mathrm{E}+12)/(4+4)}{(7.79272 \mathrm{E}+12 + 2.76829 \mathrm{E}+12)/(4290-8-8)} = 37.307$$

Since the Chow test is a test of whether the difference between the two regression models is statistically significant, we compare the test statistic to a critical value from the F distribution with $(k_{M}+k_{F})$ and $(n_{M}+n_{F}-2k_{M}-2k_{F})$ degrees of freedom. At a significance level of 0.05, the critical value for this test is 3.97. Since our test statistic is much larger than this critical value, we reject the null hypothesis that the two regression models are not significantly different and conclude that there is a structural break. Therefore, the best choice is D.

Figure: Suppose That in the Course of Testing Whether Salary Pooled \text { Pooled } Pooled

Figure:
Suppose That in the Course of Testing Whether Salary $\text { Pooled }$