Final answer:
The residual for a student with a high school GPA of 3.8 and a freshman GPA of 3.5, using the regression equation 10 = 0.22 + 0.72h, is 0.544. This is calculated by taking the actual GPA and subtracting the predicted GPA obtained from the regression equation.
Step-by-step explanation:
The subject of the question is to calculate the residual for a student's college GPA based on their high school GPA using a given linear regression equation. The regression equation is 10 = 0.22 + 0.72h. To find the residual, you first need to calculate the predicted freshman GPA using the student's high school GPA (h).
For a high school GPA (h) of 3.8, the predicted college GPA (u) is:
- u = 0.22 + (0.72 × 3.8)
- u = 0.22 + 2.736
- u = 2.956
The actual freshman GPA of the student is 3.5. Now, the residual is calculated as the difference between the actual GPA and the predicted GPA:
- Residual = Actual GPA - Predicted GPA
- Residual = 3.5 - 2.956
- Residual = 0.544
The residual for the student with a high school GPA of 3.8 who achieved a freshmen GPA of 3.5 is 0.544. This value represents the amount that the linear regression equation underestimated the student's freshman GPA.