Final answer:
Regression analysis is used to explore the relationship between average points per game and average minutes per game for basketball players, through calculation of a least squares regression line and subsequent prediction intervals for individual cases.
Step-by-step explanation:
To analyze the relationship between average points per game and average minutes per game, we will perform a regression analysis. The independent variable (x) will be average minutes per game, and the dependent variable (y) will be average points per game. A scatter plot will help visualize any potential relationship between these variables before calculating the least-squares regression line.
After plotting the data, we can observe whether there is a linear relationship to determine if a regression analysis is appropriate. If there appears to be a relationship, we proceed with calculating the regression equation of the form ŷ = a + bx. The correlation coefficient (r) indicates the strength and direction of the linear relationship between the variables. A significant correlation coefficient would suggest a strong relationship.
To predict outcomes such as an individual player's average points given the average minutes played, we would use the regression equation. The coefficient of determination (r²) will show the proportion of the variance in the dependent variable that is predictable from the independent variable. For an individual prediction, like estimating average points for Johnny's playtime, we would calculate the prediction interval at the desired confidence level after finding the standard error of the estimate.