Consider the following data regarding students' college GPAs and high school GPAs. The estimated regression equation is
 

Estimated College GPA=2.24+0.2908(High School GPA).

GPAsCollege GPAHigh School GPA

3.87

4.58

3.22

3.76

3.46

2.49

3.77

4.16

3.19

2.68

2.08

3.38  

Compute the sum of squared errors (SSE) for the model. Round your answer to four decimal places.

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

### 1. **Obtain the predicted College GPA values using the regression equation:**
The estimated regression equation is:
\[
\text{Estimated College GPA} = 2.24 + 0.2908(\text{High School GPA})
\]

For each high school GPA, we can calculate the corresponding predicted College GPA by substituting the High School GPA values into this equation.

### 2. **Calculate the errors (residuals):**
For each data point, subtract the predicted College GPA from the actual College GPA to get the error (residual).

\[
\text{Residual} = \text{Actual College GPA} - \text{Predicted College GPA}
\]

### 3. **Square the residuals:**
Square each of the residuals to ensure all values are positive.

\[
\text{Squared Error} = (\text{Residual})^2
\]

### 4. **Sum the squared errors:**
Finally, sum up all the squared errors to get the **sum of squared errors (SSE)**.

Let's go step-by-step to calculate it.The sum of squared errors (SSE) for the model is **1.7856**, rounded to four decimal places.

Do you want more details or have any questions about the process?

Here are 5 related questions to expand on this topic:
1. How does changing the slope of a regression equation affect the SSE?
2. What is the difference between the SSE and the total sum of squares (SST)?
3. How is the coefficient of determination \(R^2\) related to SSE?
4. What are the assumptions behind using linear regression for this type of model?
5. Can you interpret the slope in this regression equation?

**Tip:** A smaller SSE indicates that the regression model fits the data better, as the errors between the actual and predicted values are smaller.

Consider the following data regarding students' college GPAs and high school GPAs. The estimated regression equation is: Estimated College GPA = 2.24 + 0.2908(High School GPA). GPAs: College GPA: 3.87, 4.58, 3.22, 3.76, 3.46, 2.49, 3.77, 4.16, 3.19, 2.68, 2.08, 3.38. Compute the sum of squared errors (SSE) for the model. Round your answer to four decimal places.

Learn how to compute the sum of squared errors (SSE) for a linear regression model that estimates college GPAs based on high school GPAs. This problem involves applying the least squares regression theorem and understanding the error analysis for statistical models. Suitable for college-level students studying statistics or data analysis.

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