To compute the standard error of the regression model ($s_e$), we need to follow these steps:

Formula for the Standard Error of the Estimate:

$s_e = \sqrt{\frac{\sum{(y_i - \hat{y_i})^2}}{n - 2}}$ Where:

• $y_i$ is the actual value of the dependent variable (College GPA).
• $\hat{y_i}$ is the predicted value from the regression equation.
• $n$ is the number of data points (students).

We are given the estimated regression equation: $\hat{y} = 0.03 + 0.9077 \times (\text{High School GPA})$

Step 1: Predict College GPA using the regression equation for each High School GPA.

• Use the provided High School GPAs to calculate the predicted College GPA ($\hat{y_i}$) for each student.

Step 2: Calculate the residuals $(y_i - \hat{y_i})$ for each data point.

Step 3: Compute the sum of squared residuals $\sum{(y_i - \hat{y_i})^2}$.

Step 4: Calculate the standard error using the formula above.

Let's go ahead and compute these values. First, we'll calculate the predicted College GPA for each student.

High School GPAs:

• 2.08, 2.12, 2.27, 2.65, 3.97, 4.09, 3.07, 3.55, 3.46, 3.46, 3.14, 3.76

Calculating the predicted College GPAs:

$\hat{y} = 0.03 + 0.9077 \times (\text{High School GPA})$

I'll compute the predictions for each High School GPA. numpy as np

Given High School GPAs

high_school_gpa = np.array([2.08, 2.12, 2.27, 2.65, 3.97, 4.09, 3.07, 3.55, 3.46, 3.46, 3.14, 3.76])

Regression equation: College GPA = 0.03 + 0.9077 * High School GPA

intercept = 0.03 slope = 0.9077

Predicted College GPAs

predicted_college_gpa = intercept + slope * high_school_gpa predicted_college_gpaThe predicted College GPAs for each High School GPA are:

• 1.9180, 1.9543, 2.0905, 2.4354, 3.6336, 3.7425, 2.8166, 3.2523, 3.1706, 3.1706, 2.8802, 3.4429

Step 2: Calculate the residuals ($y_i - \hat{y_i}$) for each data point.

Now we can subtract the predicted College GPA from the actual College GPA values to find the residuals. Let's compute the residuals next.

I'll calculate the residuals for each student. Given actual College GPAs actual_college_gpa = np.array([2.08, 2.12, 2.27, 2.65, 3.97, 4.09, 3.07, 3.55, 3.46, 3.46, 3.14, 3.76])

Calculate residuals (actual - predicted)

residuals = actual_college_gpa - predicted_college_gpa residualsThe residuals (differences between the actual and predicted College GPAs) for each student are:

• 0.1620, 0.1657, 0.1795, 0.2146, 0.3364, 0.3475, 0.2534, 0.2977, 0.2894, 0.2894, 0.2598, 0.3170

Step 3: Calculate the sum of squared residuals ($\sum{(y_i - \hat{y_i})^2}$).

Now let's square each residual and calculate the sum of squared residuals. Square the residuals squared_residuals = residuals**2

Sum of squared residuals

sum_squared_residuals = np.sum(squared_residuals) sum_squared_residualsThe sum of squared residuals ($\sum{(y_i - \hat{y_i})^2}$) is approximately 0.8542.

Step 4: Calculate the standard error ($s_e$).

Now, we can use the formula for the standard error:

$s_e = \sqrt{\frac{\sum{(y_i - \hat{y_i})^2}}{n - 2}}$

Where $n = 12$ (the number of data points). Let's calculate $s_e$. Number of data points n = len(actual_college_gpa)

Standard error calculation

standard_error = np.sqrt(sum_squared_residuals / (n - 2)) round(standard_error, 4)It seems like I can’t do more advanced data analysis right now. Please try again later. Let me know if you would like me to walk you through the steps of calculating the standard error manually or if you have any other questions!