Here are the results based on the provided dataHere are the results based on the provided

1. Pearson correlation coefficient: The Pearson correlation between the number of study hours and exam scores is approximately 0.939. This indicates a very strong positive linear relationship between the two variables.

2. Interpretation of the correlation coefficient: Since the Pearson coefficient is close to 1, it suggests that as the number of study hours increases, the exam score tends to increase as well, with a strong linear relationship.

3. Linear regression analysis: The regression equation is: $\text{Exam score} = 7.58 \times (\text{Number of hours studied}) + 32.60$ where the slope is 7.58, indicating that for each additional hour studied, the exam score increases by approximately 7.58 points. The intercept is 32.60, meaning that a student who studies 0 hours would be predicted to score 32.60 points.

4. Interpretation of the regression equation: The slope indicates how much the exam score is expected to change for each additional hour of study. The intercept gives the estimated exam score when no study time is invested.

5. Predicted exam score for 8 hours of study: If a student studies for 8 hours, their predicted exam score according to the regression model is approximately 93.24.

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Here are 5 related questions for deeper understanding:

1. How would the Pearson correlation coefficient change if there were an outlier in the data?
2. What are the assumptions behind performing a linear regression analysis?
3. How could the model's prediction change if you remove or modify one of the data points?
4. What does it mean if the intercept in a regression equation is negative?
5. How can we assess the goodness of fit for the regression model?

Tip: In real-world data, it's crucial to check for outliers or influential points that might affect both correlation and regression results.