Correlation and Regression

Correct Answer: 0.64

The coefficient of determination, denoted as R-squared, is the square of the correlation coefficient between the independent variable and the dependent variable in a simple linear regression. In this case, the correlation coefficient is given as 0.8. To find R-squared, we need to square this value: R-squared = (0.8)^2 = 0.64 Therefore, the coefficient of determination (R-squared) is 0.64. The other answers are incorrect because they do not represent the square of the given correlation coefficient.

Correct Answer: Change in the dependent variable for a one-unit change in the independent variable

The slope coefficient in a regression analysis measures the change in the dependent variable for a one-unit change in the independent variable. The other two options are incorrect: - The proportion of variance in the dependent variable explained by the independent variable is measured by the coefficient of determination (R-squared), not the slope coefficient. - While the slope coefficient does indicate the direction (positive or negative) of the linear relationship between the variables, it does not directly measure the strength of this relationship. The strength is better measured by the correlation coefficient.

Correct Answer: There is a strong negative linear relationship between the independent and dependent variables.

Answer 254078 is correct because a correlation coefficient of -0.92 indicates a strong negative linear relationship between the independent and dependent variables. This means that as the independent variable increases, the dependent variable tends to decrease, and vice versa. Answer 254079 is incorrect because the square of the correlation coefficient (R^2) represents the proportion of variance in the dependent variable that can be explained by the independent variable. In this case, (-0.92)^2 = 0.8464, meaning that approximately 84.64% of the variation in the dependent variable can be explained by the independent variable, not 92%. Answer 254080 is incorrect because the correlation coefficient only measures the strength and direction of the linear relationship between two variables. It does not provide information about the slope of the regression line or the specific change in the dependent variable associated with a one-unit change in the independent variable.