True or False and why 1.The variability due to error (SSE) is always smaller than the...

True or False and why

1.The variability due to error (SSE) is always smaller than the variation explained by the model (SSModel).

2.If the size of the typical error increases, then the prediction interval for a new observation becomes narrower.

3. For the same value of the predictor, the 95% prediction interval for a new observation is always wider than the 95% confidence interval for the mean response.

4.If the correlation between X1 and Y is greater (in magnitude) than the correlation between X2 and Y , then the coefficient of determination for regressing Y on X1 is greater than the coefficient of determination for regressing Y on X2.

Solutions

Expert Solution

1.The variability due to error (SSE) is always smaller than the variation explained by the model (SSModel). False. (It is not always true).

2.If the size of the typical error increases, then the prediction interval for a new observation becomes narrower. False. (If size of the typical error increases i.e. margin of error of prediction interval increases hence the prediction interval for a new observation becomes wider.

3. For the same value of the predictor, the 95% prediction interval for a new observation is always wider than the 95% confidence interval for the mean response. True. Since for prediction interval the length of the interval is

Since for confidence interval the length of the interval is

the coefficient of determination for regressing Y on X1 is greater than the coefficient of determination for regressing Y on X2.

orchestra answered 1 year ago

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