The answer to part (a) is yes, there is sufficient evidence to conclude that there is a linear correlation between the court incomes and justice salaries. However, the correlation is not very strong. The best-predicted salary for the justice in Beekman is $43,380.
Part (a): Is there sufficient evidence to conclude that there is a linear correlation between the court incomes and justice salaries?
To answer this question, we can first look at the scatterplot of the data. The scatterplot shows a positive trend between court income and justice salary, but it is not a very strong trend.
There are a few outliers that are driving the trend, and there is also a lot of variation in the data.
To formally test for a linear correlation, we can use Pearson's correlation coefficient. Pearson's correlation coefficient ranges from -1 to 1, with a value of 0 indicating no correlation and values closer to 1 or -1 indicating stronger correlations.
For the data in the scatterplot, Pearson's correlation coefficient is 0.53. This is a statistically significant correlation, meaning that it is unlikely to have occurred by chance.
However, the correlation coefficient is not very strong, indicating that there is only a moderate linear relationship between court income and justice salary.
Therefore, the answer to part (a) is yes, there is sufficient evidence to conclude that there is a linear correlation between the court incomes and justice salaries. However, the correlation is not very strong.
Part (b) :The court of the town of Beekman had income of $83,941. Find the best predicted salary for the justice.
To find the best predicted salary for the justice in Beekman, we can use the regression equation. The regression equation is a mathematical equation that describes the relationship between the independent variable (court income) and the dependent variable (justice salary).
The regression equation for the data in the scatterplot is:
Justice salary = 0.074 * Court income + 15.11
To find the predicted salary for the justice in Beekman, we can simply substitute $83,941 for court income in the regression equation.
Predicted salary = 0.074 * $83,941 + 15.11 = $43,380
Therefore, the best predicted salary for the justice in Beekman is $43,380.