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(a) The percentage of the variation in \( y \) explained by the regression line is approximately **71.88%**.

(b) The correlation coefficient \( r \) is approximately **0.85**.

Would you like a detailed explanation of how these values were calculated?

Here are some related questions to consider:
1. What does a correlation coefficient of 0.85 indicate about the strength of the relationship?
2. How is the regression line affected by changes in the dataset?
3. Can you calculate the slope and intercept of the least-squares regression line from this data?
4. What is the significance of \( R^2 \) in a regression analysis?
5. How would outliers in the data affect the correlation coefficient and regression results?

**Tip**: The closer the \( r^2 \) value is to 100%, the better the regression line fits the data.

Given the following data set, let x be the explanatory variable and y be the response variable: x = [6, 3, 5, 5, 3, 5, 7], y = [6, 8, 5, 6, 7, 7, 4]. (a) If a least squares line was fitted to this data, what percentage of the variation in y would be explained by the regression line? (b) Compute the correlation coefficient r.

Learn how to calculate the percentage of variation explained by a regression line and the correlation coefficient using a sample data set. This example uses least squares regression and Pearson's correlation formula, ideal for students studying statistics at the high school or college level.

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