True or False a 39 of the total variation in Y can be explai

True or False?

a. 39% of the total variation in Y can be explained by predictors included in the regression model.

b. X1 is a significant predictor of Y.

c. Holding X2 constant, a one unit increase in X1 raises Y by 0.56 units.

d. Predicted value of Y is 0 when X1 and X2 are simultaneously 0.

e. The intercept is not significantly different from 0 in the populatio

Solution

a) True

We have Mulitiple R = 0.39 which is the value of correlation coefficient thus it tells that 39% of the total variation can be explained by the predictors.

b) True

The coefficient of X1 is - 0.56 which is a siginifucant value in the prediction of Y.

c) False

The coefficient of X1 is - 0.56 therefore keeping other variables constant, one unit increase in X1 will not raise the Y but it will result in 0.56 unit of decline in the value of Y.

d) False.

The line of regression that will be obtained from the given regression output will be,

Y = 3.65 - 0.56 X1 + 0.67 X2.

Therefore, if X1 and X2 are simultaneosly zero then also predicted value of Y will not be zero but will be equal to the intercept, that is 3.64.

e) False.

The intercept is 3.64.