# For each of the following statements, indicate whether it is true or false. If false, explain why

__QUESTION:__

For each of the following statements, indicate whether it is true or false. If false, explain why it is false. In regression analysis:

1. The estimated coefficient of x_{1} can be positive in the bivariate model but negative in a multiple regression model.

2. When a model is refitted after y = income is changed from dollars to euros, R^{2}, the correlation between y and x_{1}, the F statistics and t statistics will not change.

3. If r^{2} = 0.6 between y and x_{1} and if r^{2 }= 0.6 between y and x_{2}, then for the multiple regression model with both predictors R^{2} = 1.2.

4. The multiple correlations between y and ŷ can equal -0.40.

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__ANSWER:__

1. True

2. True

3. False; R-squared cannot exceed 1

4. False; the predicted values ŷ cannot correlate negatively with y. Otherwise, the predictions would be worse than merely using y to predict y̅.

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