31. A financial analyst theorizes that commute × increase as the percentage of land availability for homes in a city decreases. To test this theory, the analyst uses a regression analysis. Which analysis result is supportive of this analyst's theory?
Answer: C
The R-squared value is 0.90.
A high R-squared value of 0.90 suggests that 90% of the variance in the dependent variable (commute increase) can be explained by the independent variable (land availability for homes). This strong correlation supports the analyst's theory that as land availability decreases, commute times increase.
A) The R-squared value is 0.10.
An R-squared value of 0.10 indicates that only 10% of the variance in the dependent variable can be explained by the independent variable. This weak correlation does not support the analyst's theory, as it suggests a minimal relationship between land availability and commute times.
B) The P-value for the regression coefficient is 0.50.
A P-value of 0.50 suggests that the relationship between the independent and dependent variables is not statistically significant. This indicates that there is insufficient evidence to support the analyst's theory regarding the effect of land availability on commute times.
C) The R-squared value is 0.90.
This option accurately reflects a strong explanatory power of the model, indicating a robust relationship between land availability and commute increase. A high R-squared value supports the analyst's theory effectively.
D) The P-value for the regression coefficient is 1.
A P-value of 1 indicates that the independent variable has no effect on the dependent variable, meaning there is no statistically significant relationship. This null result directly contradicts the analyst's theory that decreasing land availability impacts commute times.
Conclusion
The R-squared value of 0.90 is definitive evidence supporting the analyst's theory, as it demonstrates a strong correlation between the decrease in land availability and the increase in commute times. In contrast, the other options either indicate weak or no significant relationships, failing to provide any support for the theory being tested.