Question

A study to see if the IQ can be used to predict grade-point average (GPA) found the following: Mean of the IQ's = 108.9, sIQ, = 13.2, Mean of the GPA's = 2.3, sGPA, = 0.5. Further, r2 = 0.75. The regression line will pass through the point:

Answer 1

The regression line in the study predicting GPA from IQ scores will pass through the point with the mean IQ of 108.9 and the mean GPA of 2.3, specifically (108.9, 2.3). The coefficient of determination (r^2 = 0.75) indicates that 75% of the variance in GPA is explained by IQ.

Step-by-step explanation:

To determine the point through which the regression line will pass, we use the means of the two variables in question. Since the regression line estimates the relationship between IQ and GPA, the line must pass through the point that represents the means of these variables on a scatterplot. In this case, the means given are a mean IQ of 108.9 and a mean GPA of 2.3. Therefore, the regression line will pass through the point (108.9, 2.3).

It is important to note that the coefficient of determination, r^2, in this study is 0.75. This means that 75% of the variance in GPA can be explained by the IQ scores. The remaining 25% is due to other factors. The coefficient of determination is a key concept in regression analysis which reflects the proportion of the variance for the dependent variable (GPA) that's predicted from the independent variable (IQ).