To compute the Sum of Squared Errors (SSE), we need to follow these steps:

1. Find the regression model: In this case, we need to assume that a linear regression model relates High School GPA (X) to College GPA (Y). The formula for a linear regression line is: $Y = a + bX$ where $a$ is the y-intercept and $b$ is the slope.

2. Compute the slope (b) and intercept (a) using the following formulas: $b = \frac{n(\sum XY) - (\sum X)(\sum Y)}{n(\sum X^2) - (\sum X)^2}$ $a = \frac{\sum Y - b(\sum X)}{n}$ where $n$ is the number of data points.

3. Calculate the predicted College GPA for each High School GPA (X) using the regression equation $Y_{\text{pred}} = a + bX$.

4. Calculate the squared errors for each data point, which is: $\text{Squared Error} = (Y_{\text{actual}} - Y_{\text{pred}})^2$

5. Sum the squared errors to find the SSE.

Let's break down the data:

High School GPA (X)	College GPA (Y)
3.28	3.20
4.75	3.95
2.22	2.89
3.79	3.68
2.74	3.94
4.90	2.37

Now I will compute the necessary values and the SSE for you. numpy as np

Given data

X = np.array([3.28, 4.75, 2.22, 3.79, 2.74, 4.90]) # High School GPA Y = np.array([3.20, 3.95, 2.89, 3.68, 3.94, 2.37]) # College GPA

Calculate necessary sums

n = len(X) sum_X = np.sum(X) sum_Y = np.sum(Y) sum_XY = np.sum(X * Y) sum_X_squared = np.sum(X ** 2)

Calculate slope (b) and intercept (a)

b = (n * sum_XY - sum_X * sum_Y) / (n * sum_X_squared - sum_X**2) a = (sum_Y - b * sum_X) / n

Predicted Y values

Y_pred = a + b * X

Calculate squared errors

squared_errors = (Y - Y_pred) ** 2

Sum of squared errors (SSE)

SSE = np.sum(squared_errors) round(SSE, 4)The Sum of Squared Errors (SSE) for the model is 1.9901.

Would you like a detailed breakdown of the steps involved or any clarifications? Here are some related questions that might help:

1. How would you compute the coefficient of determination (R²) for this regression model?
2. What is the interpretation of the slope and intercept in this context?
3. How can you perform this calculation manually without using a programming tool?
4. What other types of regression models could be applied to this data?
5. How can you evaluate if this regression model is a good fit for the data?

Tip: Always ensure that the data is suitable for linear regression by checking for a linear relationship visually (e.g., via a scatter plot).