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We are interested in predicting the concentration of a chemical in the soil (y) based on the distance from the site of chemical spill.  Suppose the following regression line was obtained based on data collected at 8 different distances from the spill site.  Find and interpret the value of the correlation coefficient. 


To find and interpret the value of the correlation coefficient (\(r\)), we can start with the \(R^2\) value provided in the summary of fit. The \(R^2\) value is the square of the correlation coefficient \(r\).

From the provided data, we have:

\[ R^2 = 0.941917 \]

To find the correlation coefficient \(r\):

\[ r = \sqrt{R^2} \]
\[ r = \sqrt{0.941917} \]
\[ r \approx 0.9705 \]

Since the slope of the regression line is negative, the correlation coefficient will also be negative:

\[ r \approx -0.9705 \]

**Interpretation:**
The correlation coefficient of approximately \(-0.9705\) indicates a strong negative linear relationship between the concentration of the chemical in the soil and the distance from the site of the chemical spill. As the distance from the spill site increases, the concentration of the chemical decreases significantly.

Would you like to ask for more details or have any other questions? Here are some additional questions you might consider:

1. What is the significance of the slope in this regression analysis?
2. How do you interpret the p-values in the parameter estimates table?
3. What steps would you take if you suspected multicollinearity in a multiple regression model?
4. How can you use this regression model to make predictions?
5. What are some potential limitations of this regression analysis?

**Tip:** When interpreting regression results, always consider both the statistical significance (p-values) and the practical significance (magnitude and direction of coefficients) of the predictors.

Learn how to interpret the correlation coefficient in regression analysis using real-world data on chemical concentration in soil relative to distance from a spill site. This problem covers statistical concepts such as correlation coefficient, linear regression, and coefficient of determination (R^2). Suitable for advanced high school students and beyond.

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