Question

What are some measures that summarize how well the sample regression equation fits the data?

A. Goodness-of-fit
B. Predictor variables
C. Dummy variables
D. Regression

Answer 1

The measures that summarize how well the sample regression equation fits the data are the slope of the regression equation, the y-intercept of the regression equation, the correlation coefficient, and the coefficient of determination.

Step-by-step explanation:

The measures that summarize how well the sample regression equation fits the data include:

• The slope of the regression equation: The slope represents the change in the dependent variable (y) for every one unit change in the independent variable (x). It tells us the direction and steepness of the relationship.
• The y-intercept of the regression equation: The y-intercept represents the value of the dependent variable when the independent variable is zero. It gives us the starting point of the regression line.
• The correlation coefficient, r: The correlation coefficient measures the strength and direction of the linear relationship between the independent and dependent variables. It ranges from -1 to 1, with a value closer to -1 or 1 indicating a stronger relationship.
• The coefficient of determination, r-squared (r²): The coefficient of determination represents the proportion of the variability in the dependent variable that is explained by the regression equation. It ranges from 0 to 1, with a value closer to 1 indicating a better fit of the regression equation to the data.