Final answer:
The correct interpretation of the 93.47% statistic in regression output is the percentage of variance in the dependent variable explained by the independent variable, which is the coefficient of determination (r²). This captures the proportion of variance accounted for by the regression line, and the correct option is (a).
Step-by-step explanation:
The statistic 93.47% in the regression output is the percentage of variance in the dependent variable explained by the independent variable.
This is known as the coefficient of determination, or r², which, when expressed as a percentage, represents the extent to which variation in the predicted variable (y) can be explained by the independent variable (x) using the regression line. To illustrate, consider a scenario where the coefficient of determination (r²) is 0.4397, indicating that approximately 44 percent of the variance in the final exam grades is explained by the grades on the third exam, using the regression line.
Therefore, the correct interpretation of the 93.47% statistic in regression output is (a) The percentage of variance in the dependent variable explained by the independent variable, not the probability of an event, the correlation coefficient, or the margin of error. The remaining variance represents the portion that is not captured by the model. Notably, the r² value is squared from the correlation coefficient (r), and it does not give any information about the probability of an event occurring or the accuracy of the predictors in terms of margin of error.