Final answer:
The claim that a lower R2 value indicates a better ability for a regression model to predict data is false. A higher R2 value shows a better fit, and the closer the correlation coefficient, r, is to 1, the stronger the relationship and the model's predictive power.
Step-by-step explanation:
The statement 'The lower the R2 value, the better the ability of the regression model to predict the data.' is False. A lower R2 value indicates that the model is a worse fit and has less predictive accuracy. Instead, a higher R2 value suggests a better fit. The coefficient of determination, R2, represents the percentage of variation in the dependent variable that can be explained by variation in the independent variable using the regression line.
For example, if the slope of the regression line changes from 4.83 to 7.39, this may indicate a significant change, which is further explained by looking at the r-values. Considering that the new r-value is r = 0.9121, it demonstrates a stronger correlation compared to the initial r-value of r = 0.6631, as r = 0.9121 is closer to 1. This results in a stronger and more accurate predictive regression model.
The correlation coefficient, r, and the coefficient of determination, R2, are thus critical in determining the fit of a regression model. For example, if the correlation coefficient is r = -0.624 for a dataset with 14 points, the significance can be assessed by comparing it to the critical values determined by a Table of Critical Values. If r is outside these critical values, the line can be used for prediction confidently.