55. 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: D
The R-squared value is 0.90.
An R-squared value of 0.90 indicates a strong correlation between the variables in the regression analysis, suggesting that a significant percentage of the variance in commute can be explained by the percentage of land availability for homes. This supports the analyst's theory that as land availability decreases, commute times increase.
A) The P value for the regression coefficient is 1.
A P value of 1 indicates no statistical significance, meaning that the regression coefficient does not reliably predict the relationship between the variables. This does not support the analyst's theory, as it suggests that changes in land availability have no effect on commute times.
B) The R-squared value is 0.10.
An R-squared value of 0.10 indicates a weak relationship, suggesting that only 10% of the variance in commute is explained by the percentage of land availability. This weak correlation does not support the analyst's theory, as it fails to demonstrate a clear connection between the two variables.
C) The P value for the regression coefficient is 0.50.
A P value of 0.50 suggests that the regression coefficient is not statistically significant, indicating that there is a 50% chance that the observed relationship could occur by random chance. This result does not provide support for the analyst's theory, as it implies a lack of evidence for the hypothesized relationship.
D) The R-squared value is 0.90.
An R-squared value of 0.90 signifies a very strong relationship between the variables, meaning that the majority of the variance in commute can be attributed to land availability. This strongly supports the analyst's theory that a decrease in land availability leads to increased commute times.
Conclusion
The analysis result with an R-squared value of 0.90 clearly indicates a robust relationship between the percentage of land availability and commute times, validating the analyst's theory. In contrast, the other options reflect either a lack of significance or weak correlations, thus failing to support the theory effectively.