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The task involves calculating the standard error of the regression model, which is given as:

\[
\text{Estimated College GPA} = 2.74 + 0.1655 \times (\text{High School GPA})
\]

We are provided with data for both College GPA and High School GPA to compute the standard error of the model (\( s_e \)).

The steps for computing the standard error of the regression (\( s_e \)) are as follows:

1. **Use the regression equation to predict the College GPA** using the given High School GPAs.
   
   \[
   \hat{y} = 2.74 + 0.1655 \times (\text{High School GPA})
   \]

2. **Calculate the residuals (errors)** between the actual College GPAs and the predicted GPAs:

   \[
   \text{Residual} = y - \hat{y}
   \]
   where \( y \) is the actual College GPA and \( \hat{y} \) is the predicted College GPA.

3. **Square each residual** to get the squared residuals.

4. **Find the sum of squared residuals (SSR)**.

5. **Compute the standard error** using the formula:

   \[
   s_e = \sqrt{\frac{\sum (\text{Residuals}^2)}{n - 2}}
   \]
   where \( n \) is the number of data points (in this case, \( n = 6 \)).

I'll calculate the standard error for you based on this data.The standard error of the regression model (\( s_e \)) is approximately 0.4242 when rounded to four decimal places.

Would you like a detailed breakdown of the calculations, or do you have any questions?

Here are five related questions to expand your understanding:

1. How does the standard error of the regression model help in understanding the fit of the model?
2. What would happen to the standard error if we had more data points?
3. How do you interpret a high versus low standard error in this context?
4. Can you compute confidence intervals for the predictions using this standard error?
5. What are other measures of fit besides standard error, such as \( R^2 \)?

**Tip**: The standard error tells you how well the regression model's predictions match the actual data. The smaller the standard error, the closer the predicted values are to the actual values.

Consider the following data regarding students' college GPAs and high school GPAs. The estimated regression equation is Estimated College GPA = 2.74 + 0.1655 (High School GPA). Compute the standard error of the model.

Learn how to calculate the standard error for a regression model predicting college GPA based on high school GPA. This problem involves key statistical concepts like regression analysis and residuals. It’s suitable for students at the high school or college level.

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