for a fixed sample size as the number of indeoendent variables in a regression model increases...

for a fixed sample size as the number of indeoendent variables in a regression model increases the power of the regression decreases. T or F

The width of a 95% confidence interval around a relative risk increases as the sample size decreases. T or F

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Expert Solution

1) True ...

R2 increases with the increase in the number of predictors used in the model, even if those variables are only weakly associated with the response. And including those predictors [which do not significantly contribute to the model for predicting the response] leads to ‘overfitting’ issue.

This is due to the fact that adding another variable to the least squares equations must allow us to fit the training data (though not necessarily the testing data) more accurately. Thus, the R2 statistic, which is also computed on the training data, must increase. Hence, in case of MRA (multiple regression analysis), it is suggested to look for improvement in the value of adjusted R2. Other measures for accuracy/fit of the model may be RSE, p-value for ANOVA (F-statistics).

2) True.....Increasing the sample size decreases the width of confidence intervals, because it decreases the standard error.

milcah answered 9 months ago

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