The following table was generated from the sample data of 10 junior high students regarding the average number of hours they are unsupervised per night, the average number of hours they play video games per night, and their final grades in their math class. The dependent variable is the final grade, the first independent variable (x1) is the number of hours unsupervised each night, and the second independent variable (x2) is the number of hours of video games each night.

CoefficientsStandard Errort-Statp-valueIntercept

90.056561

7.327333

12.290496

0.000005

Hours Unsupervised

−4.395928

1.235022

−3.559393

0.009227

Hours Playing Video Games

1.089593

1.840141

0.592125

0.572388

To estimate the final grade \( y \) when given the number of hours unsupervised per night (\( x_1 \)) and the number of hours spent playing video games per night (\( x_2 \)), you would use the following linear regression equation:

\[
y = \text{Intercept} + (\text{Coefficient for } x_1) \times x_1 + (\text{Coefficient for } x_2) \times x_2
\]

Based on the table you provided, the equation becomes:

\[
y = 90.056561 - 4.395928 \times x_1 + 1.089593 \times x_2
\]

Now, to estimate the value of \( y \) when \( x_1 = 32 \) (hours unsupervised) and \( x_2 = \) (hours playing video games), please provide the value for \( x_2 \). If the assumption is that \( x_2 = 0 \), then we can proceed with the calculations.

Would you like to proceed with \( x_2 = 0 \), or do you have a different value in mind?

Once I have \( x_2 \), I can calculate the estimated final grade and round it to three decimal places.

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Would you like details on this process, or do you have any other questions?

Here are some related questions that might interest you:
1. How do you interpret the coefficients in a linear regression model?
2. What does the p-value tell us about the significance of an independent variable?
3. How would you predict the final grade if the student plays more video games?
4. What is multicollinearity, and how does it affect regression analysis?
5. How can the standard error of a coefficient affect the reliability of the estimate?
6. What is the R-squared value, and how does it relate to the regression model?
7. How would you adjust the model if you added another independent variable?
8. How can you test the accuracy of your regression model?

**Tip:** When working with regression models, it's important to consider the significance of each variable (p-value) to understand their impact on the dependent variable.

Explore how linear regression predicts final grades based on hours unsupervised and hours playing video games. Learn to interpret coefficients, assess significance, and estimate outcomes. Suitable for advanced high school students.

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