A researcher's results are shown below using Femlab (labor force participation rate among females) to try to predict Cancer (death rate per 100,000 population due to cancer) in the 50 U.S. states. $$\begin{array} { l r }
\hline { \text { Regression Statistics } } \
\hline \text { Multiple R } & 0.313422848 \
\text { R Square } & 0.098233882 \
\text { Adjusted R Square } & 0.079447088 \
\text { Standard Error } & 32.07003698 \
\text { Observations } & 50 \
\hline
\end{array}$$ $$\begin{array} { l c r r }
\hline \text { Variable } & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } \
\hline \text { Intercept } & 343.619889 & 61.0823514 & 5.62552 \
\text { Femlab } & - 2.2833659 & 0.99855319 & - 2.28667 \
\hline
\end{array}$$ Which statement is valid regarding the relationship between Femlab and Cancer?
A)A rise in female labor participation rate will cause the cancer rate to decrease within a state.
B)This model explains about 10 percent of the variation in state cancer rates.
C)At the .05 level of significance, there isn't enough evidence to say the two variables are related.
D)If your sister starts working, the cancer rate in your state will decline.

Question

A researcher's results are shown below using Femlab (labor force participation rate among females) to try to predict Cancer (death rate per 100,000 population due to cancer) in the 50 U.S. states. $$\begin{array} { l r } 
\hline { \text { Regression Statistics } } \
\hline \text { Multiple R } & 0.313422848 \
\text { R Square } & 0.098233882 \
\text { Adjusted R Square } & 0.079447088 \
\text { Standard Error } & 32.07003698 \
\text { Observations } & 50 \
\hline
\end{array}$$ $$\begin{array} { l c r r } 
\hline \text { Variable } & \text { Coefficients } & \text { Standard Error } &  { t \text { Stat } } \
\hline \text { Intercept } & 343.619889 & 61.0823514 & 5.62552 \
\text { Femlab } & - 2.2833659 & 0.99855319 & - 2.28667 \
\hline
\end{array}$$ Which statement is valid regarding the relationship between Femlab and Cancer?
A)A rise in female labor participation rate will cause the cancer rate to decrease within a state.
B)This model explains about 10 percent of the variation in state cancer rates.
C)At the .05 level of significance, there isn't enough evidence to say the two variables are related.
D)If your sister starts working, the cancer rate in your state will decline.

Quizplus · Accepted Answer

The R square value of 0.098 indicates that only about 10 percent of the variation in cancer rates can be explained by Femlab. This suggests a weak relationship between the two variables. Option A is incorrect as the negative coefficient for Femlab suggests that there is a negative relationship between the two variables - as the labor force participation rate of females increases, the cancer rate is expected to decrease slightly. Option C is also incorrect as although the relationship is weak, the t-statistic associated with Femlab is -2.28667, which is significant at the 0.05 level. Option D is irrelevant and does not provide any meaningful information about the relationship between the two variables.

A Researcher's Results Are Shown Below Using Femlab (Labor Force