Final answer:
The regression equation given is ŷ = -173.51 + 4.83x. For a homework grade of 64, the predicted test grade is 135 (rounded to the nearest integer), based on the provided least-squares regression line equation.
Step-by-step explanation:
The question asks about how to find the regression equation and predict a test grade based on a given homework grade using linear regression. To find the linear regression equation, we typically use the least-squares method to minimize the total distance between our line and the observed data points in the scatter plot. The least-squares regression line equation provided in the question is ŷ = -173.51 + 4.83x.
To predict the test grade for a student with a homework grade of 64, we substitute x = 64 into the equation:
Predicted test grade, ŷ = -173.51 + 4.83(64) = -173.51 + 308.92 = 135.41. When rounded to the nearest integer, the predicted test grade will be 135.
If the correlation coefficient (r) is significantly different from zero, it suggests that there is a significant linear relationship between the third exam score (x) and the final exam score (y).
However, predictions should only be made within the domain of the observed x values to ensure reliability.