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?
The R-squared value is 0.90.
A high R-squared value indicates a strong correlation between the variables being analyzed. In this case, an R-squared value of 0.90 suggests that 90% of the variance in the dependent variable (commute) can be explained by changes in the independent variable (land availability), strongly supporting the analyst's theory.
An R-squared value of 0.10 indicates that only 10% of the variance in the dependent variable is explained by the independent variable, suggesting a very weak relationship. This low value does not support the analyst's theory as it implies that land availability has minimal influence on commute times.
A P-value of 0.50 indicates that there is a 50% probability that the observed relationship could be due to random chance. This is far above the commonly accepted threshold of 0.05 for statistical significance, meaning it does not provide support for the analyst's theory regarding the impact of land availability on commute.
As explained, this high R-squared value of 0.90 demonstrates a strong explanatory power of the model, indicating that the relationship between commute times and land availability is robust and supports the analyst’s theory effectively.
A P-value of 1 suggests that the regression coefficient is not statistically significant at all, indicating no relationship between the variables. This result strongly contradicts the analyst's theory and provides no support for the hypothesis being tested.
In regression analysis, a high R-squared value is crucial for validating the relationship between the variables in question. In this scenario, an R-squared value of 0.90 indicates a strong correlation, supporting the financial analyst's theory about the influence of land availability on commute times. Conversely, low R-squared values and high P-values suggest weak or non-significant relationships, failing to lend credibility to the analyst's assertions.
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