To compute the sum of squared errors (SSE) for the model, we need to follow these steps:

Steps:

1. Calculate the predicted College GPA using the estimated regression equation for each data point.

   $\text{Estimated College GPA} = 1.99 + 0.3156 \times (\text{High School GPA})$

2. Find the error (residual) for each data point by subtracting the predicted College GPA from the actual College GPA:

   $\text{Error (Residual)} = \text{Actual College GPA} - \text{Predicted College GPA}$

3. Square the errors for each data point to get the squared error.

4. Sum the squared errors to get SSE:

   $\text{SSE} = \sum (\text{Squared Errors})$

Data provided:

College GPA	High School GPA
2.58	2.77
3.72	4.83
3.20	2.65
3.40	4.81
2.82	3.62
3.29	3.64

Let me now compute the values step by step. numpy as np

Data

college_gpa = np.array([2.58, 3.72, 3.20, 3.40, 2.82, 3.29]) high_school_gpa = np.array([2.77, 4.83, 2.65, 4.81, 3.62, 3.64])

Regression equation: Estimated College GPA = 1.99 + 0.3156 * High School GPA

predicted_college_gpa = 1.99 + 0.3156 * high_school_gpa

Calculate the errors (residuals)

errors = college_gpa - predicted_college_gpa

Square the errors

squared_errors = errors**2

Calculate SSE (sum of squared errors)

sse = np.sum(squared_errors) round(sse, 4)The sum of squared errors (SSE) for the model is 0.3949.

Would you like any further details on the calculation or the interpretation?

Here are 5 related questions to explore:

1. How do we interpret the regression equation in the context of this model?
2. What is the difference between SSE and the coefficient of determination (R²)?
3. How would the SSE change if we had a different regression model?
4. How can we compute the root mean squared error (RMSE)?
5. What does a smaller SSE imply about the quality of the regression model?

Tip: The smaller the SSE, the better the regression model fits the data since the residuals (errors) are smaller.