Final answer:
A regression model with a p-value of 0.026, which is less than the significance level of 0.05, indicates a significant linear relationship between the variables. The t-statistic supports this, showing the model is reliable for prediction. Both p-value and t-statistic criteria should be used together to assess the best model.
Step-by-step explanation:
Using the given p-value of 0.026 in regression analysis to predict credit scores, we conclude that there's a significant linear relationship between the variables considered, as this value is less than the generally accepted significance level (α) of 0.05.
The t-statistic supports this conclusion and implies that the regression model with these predictors is likely reliable. According to the information provided, if, for example, we computed a correlation coefficient (r) of 0.801 with n = 10 data points (df = 8), and using critical value tables we found that this r is above the critical value of 0.632, we can affirm that the relationship is statistically significant and use the regression line for prediction.
Comparing models using both p-value and t-statistic criteria is essential. A model that meets both criteria is robust and more likely preferable for predicting outcomes accurately.
For instance, in a university admissions scenario, correlating current students' GPA with standardized test scores helps in predicting the success of applicants.
Therefore, considering both criteria, we would choose the model that indicates both a low p-value and a high t-statistic, confirming its reliability in the sample data and for making predictions