Question

Which of the following statements about the regression standard error hold TRUE? (2p)
I. The regression standard error reflects the variation of the y-values about the regression line.
II. The regression standard error is an estimate of the model standard deviation .
III. The larger the regression standard error is, the better the model fits the data and the more precise inference about the regression model will be.
A) I
B) I and II
C) II and III
D) I, II, and III

In multiple regression analysis, if the model provides good fit, this indicates that the: (1p)
A) sum of squares for error will be small.
B) value of the regression standard error will be small.
C) squared multiple regression correlation value is will be close to 1 or –1.
D) All of the answers are correct.

If multicollinearity is present, then we can conclude that the fitted regression model: (1p)
A) may have estimated slopes very different from what we should expect due to numerical instabilities, making correct interpretation of the effect on the response variable more difficult.
B) will have a very low   value.
C) is not useful at all and will have a very low   value.
D) may have estimated slopes very different from what we should expect due to numerical instabilities, making correct interpretation of the effect on the response variable more difficult, and contains redundant information due to two or more highly correlated explanatory variables.

Answer 1

1: ( B) Option is correct, because the standard error of the regression also known as the standard error of the estimate,represents the average distance that the observed values fall from the regression line.

2:(A)Option is correct because model is best fit when sum of square of error will be minimum. R^2 lies from 0 to1.so c is not correct.

3:(d) option is correct because multicollinearity occur when two independent variable are correlated to each other. Then multicillinearity affect the result of estimated coefficient because variance of estimated coefficientt is large.