Question

If a data set of 10 observations is used in a multiple regression analysis with 10 independent variables, then _______. Multiple Choice R2 will be equal to 1.0 the multiple standard error of the estimate will be 1.0 the independent variables will be correlated the regression coefficients will all equal 1.0

Answer 1

R² will be 1.0

Explanation:

R² is used to explain the variation in dependent variable of the regression model. If n number of observation are present and we include n independent variable then there will be no variability to capture and thus R² shows that all the variations is explained by the regression model and thus for this purpose our R² value will be 1.0. R²=1 is explained as there is 100% variation in dependent variable is explained by regression model. You can see that as you increase the number of independent variable in your data then R² values increases and if you include 10 independent variable for 10 observation then R² will be 1.