To analyze the relationship between average income per person and governor salary based on the provided data:
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Residual Plot: The residual plot helps to determine if a linear model is an appropriate fit. If the residuals are randomly scattered around zero, this indicates that the linear model fits the data well. If there are patterns or systematic trends in the residuals (e.g., a curve), it suggests that the linear model is not a good fit. Since the details of the residual plot aren't provided, I can't definitively conclude whether the function \(y = 0.35x + 128.05\) is appropriate without seeing how the residuals behave.
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Correlation Coefficient: The correlation coefficient \(r = 0.15\) indicates the strength and direction of the linear relationship between the two variables. A value of \(0.15\) is very close to zero, which suggests that there is a very weak positive linear correlation. Therefore, the correct answer related to the correlation coefficient is "weak and positive linear correlation."
Summary:
- The residual plot does or does not indicate that the function \(y = 0.35x + 128.05\) is an appropriate fit (depends on the characteristics of the residuals from the plot).
- The correlation coefficient \(r = 0.15\) indicates a weak and positive linear correlation between average income per person and governor salary in different states.