Question

Which of the following statements are not correct? The coefficient of determination, denoted by rA2 is interpreted as the proportion of observed y tion that cannot be explained by the simple linear regression model. The higher the value of the coefficient of determination, the more successful is the simple linear regression model in explaining y variation. f the coefficient of determination is small, an analyst will usually want to search for an alternative model (either a nonlinear model or a multiple regression model that involves more than a single independent variable). The coefficient of determination can assume any value between 0 and 1, inclusive. All of the above statements are correct.

Which of the following statements are not correct? The coefficient of determination, denoted by r^2 is interpreted as the proportion of observed y variation that cannot be explained by the simple linear regression model. The higher the value of the coefficient of determination, the more successful is the simple linear regression model in explaining y variation. If the coefficient of determination is small, an analyst will usually want to search for an alternative model (either a nonlinear model or a multiple regression model that involves more than a single independent variable). The coefficient of determination can assume any value between 0 and 1, inclusive. All of the above statements are correct.

Answer 1

ans) e) All of the above statements are correct.

The coefficient of determination (denoted by R²) is a key output of regression analysis. It is interpreted as the proportion of the variance in the dependent variable that is predictable from the independent variable.

• The coefficient of determination is the square of the correlation (r) between predicted y scores and actual y scores; thus, it ranges from 0 to 1.
• With linear regression, the coefficient of determination is also equal to the square of the correlation between x and y scores.
• An R² of 0 means that the dependent variable cannot be predicted from the independent variable.
• An R² of 1 means the dependent variable can be predicted without error from the independent variable.
• An R² between 0 and 1 indicates the extent to which the dependent variable is predictable. An R² of 0.10 means that 10 percent of the variance in Y is predictable from X; an R² of 0.20 means that 20 percent is predictable; and so on.