The table shown lists each states average income per person and the governors salary for each state, as of 2020, in thousands.

Question

state average income (in dollars) governor salary (in thousand of dollars)
kentucky 47.1 152.2
mississippi 42.3 122.2
minnesota 61.5 127.6
texas 55.4 153.8
utah 51.7 160.7
Rhode island 58.7 145.8
michigan 52.7 159.3
ohio 53.2 159.2
idaho 48.2 138.3
The graph of average income per person and governor salary of each state is shown in a scatter plot and residual plot of this data set. The equation of the line of best fit that models the relationship between the average income per person and governors salary in different states is y = 0.35x + 128.05.
A residual plot is created of this data
Part A: The residual plot (indicates or does not indicate) that the function y = 0.35x + 128.05 is an appropriate fit for the data. The correlation coefficient, r = 0.15 indicates a (strong and positive linear correlation, strong and negative linear correlation, moderate and positive linear correlation, moderate and negative linear correlation, weak and positive linear correlation or nonlinear correlation) between average income per person and governors salary in different states.

Answer 1

To analyze the relationship between average income per person and governor salary based on the provided data:

1. 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.

2. 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.