The prediction equation, based on the data provided, is:

$\hat{y} = 3.031 + 0.043 \times (\text{Study Time}) - 0.079 \times (\text{Skipped Classes})$

Where:

• $\hat{y}$ is the predicted GPA.
• $3.031$ is the intercept ($\beta_0$).
• $0.043$ is the slope for Study Time ($\beta_1$).
• $-0.079$ is the slope for Skipped Classes ($\beta_2$).

Interpretation of the Slope:

• Study Time Slope ($\beta_1 = 0.043$): For each additional hour of study time, the GPA is expected to increase by approximately 0.043, holding the number of skipped classes constant.
• Skipped Classes Slope ($\beta_2 = -0.079$): For each additional class skipped, the GPA is expected to decrease by approximately 0.079, holding study time constant.

Would you like more details or have any questions?

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Here are some related questions you might find helpful:

1. How can we interpret the intercept value in the context of this problem?
2. How would the prediction equation change if we only considered one predictor variable?
3. What impact do outliers have on the prediction equation?
4. How can we calculate the predicted GPA for a specific student?
5. What assumptions are required for the accuracy of this prediction equation?
6. How do you determine the statistical significance of the slopes?
7. What is the coefficient of determination ($R^2$) for this model?
8. How might multicollinearity affect this prediction model?

Tip: To better understand the impact of each predictor, consider plotting the data and the regression plane to visualize the relationship between study time, skipped classes, and GPA.