[DATA] CEO Performance (Refer to Problem 33 in Section 4.1) The following data represent the total compensation for 12 randomly selected chief executive officers (CEOs) and the company’s stock performance in 2017.

d. Based on your results to parts (b) and (c), would you recommend using the least-squares regression line to predict the stock return of a company based on the CEO’s compensation? Why?

Verified step by step guidance

1. Step 1: Review the results from parts (b) and (c), which likely include the least-squares regression line equation and the correlation coefficient (r) or coefficient of determination (r^2). These statistics summarize the relationship between CEO compensation and stock return.
2. Step 2: Interpret the correlation coefficient (r) or r^2 value to understand the strength and direction of the linear relationship. A value close to 1 or -1 indicates a strong linear relationship, while a value near 0 indicates a weak relationship.
3. Step 3: Examine the residuals or any diagnostic plots (if available) to check for patterns that might violate the assumptions of linear regression, such as non-linearity, heteroscedasticity, or outliers.
4. Step 4: Consider the practical significance of the regression line. Even if the statistical relationship is significant, assess whether the CEO compensation is a meaningful predictor of stock return based on the size of the slope and the variability explained.
5. Step 5: Based on the above analyses, decide whether the least-squares regression line is appropriate for prediction. If the relationship is weak, residuals show patterns, or the model explains little variability, it would not be recommended to use the regression line for prediction.

Key Concepts

Least-Squares Regression Line

The least-squares regression line is a statistical method used to model the relationship between two variables by minimizing the sum of the squares of the vertical distances of the points from the line. It helps predict the value of a dependent variable based on an independent variable. In this context, it predicts stock return based on CEO compensation.

Correlation and Strength of Relationship

Correlation measures the strength and direction of a linear relationship between two variables, ranging from -1 to 1. A strong correlation indicates that the regression line is a good predictor, while a weak correlation suggests poor predictive power. Understanding correlation helps assess if CEO compensation is related to stock return.

Residuals and Model Appropriateness

Residuals are the differences between observed values and predicted values from the regression line. Analyzing residuals helps determine if the model fits well or if there are patterns indicating poor fit. Large or systematic residuals suggest the least-squares regression line may not be appropriate for prediction.