Question

"Constructing and Interpreting a Prediction Interval In Exercises 21-30, construct the indicated prediction interval and interpret the results.
21. Proceeds Construct a 95% prediction interval for the proceeds from initial public offerings in Exercise 11 when the number of offerings is 200."

Accepted Answer

Identify the regression model from Exercise 11, including the estimated regression equation and the standard error of the estimate (often denoted as $$ s  or$$ $$ s_e ). $$This model relates the number of offerings to the proceeds. Calculate the predicted value $$ \hat{y} $$ for the number of offerings $$ x = 200  by $$substituting $$ x = 200 $$ into the regression equation: $$ \hat{y} = b_0 + b_1 	imes 200 $$, where $$ b_0  is $$the intercept and $$ b_1  is $$the slope. Determine the critical value $$ t^* $$ from the t-distribution for a 95% prediction interval, using the appropriate degrees of freedom (usually $$ n - 2 $$, where $$ n  is $$the sample size from Exercise 11). Calculate the standard error of the prediction interval using the formula: $$ SE_{pred} = s \sqrt{1 + \frac{1}{n} + \frac{(200 - \bar{x})^2}{\sum (x_i - \bar{x})^2}} $$, where $$ \bar{x}  is $$the mean of the $$ x -$$values and $$ \sum (x_i - \bar{x})^2  is $$the sum of squared deviations of the $$ x -$$values. Construct the 95% prediction interval using the formula: $$ \hat{y} \pm t^* 	imes SE_{pred} . $$Interpret this interval as the range in which we expect the proceeds from 200 offerings to fall with 95% confidence, considering both the uncertainty in the regression and the variability of individual observations.

"Constructing and Interpreting a Prediction Interval In Exercises 21-30, construct the indicated prediction interval and interpret the results.
21. Proceeds Construct a 95% prediction interval for the proceeds from initial public offerings in Exercise 11 when the number of offerings is 200."

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Concetti chiave

Prediction Interval

Confidence Level

Application to Regression or Forecasting

"Constructing and Interpreting a Prediction Interval In Exercises 21-30, construct the indicated prediction interval and interpret the results.21. Proceeds Construct a 95% prediction interval for the proceeds from initial public offerings in Exercise 11 when the number of offerings is 200."

Risposta video verificata per un problema simile:

Concetti chiave

Prediction Interval

Confidence Level

Application to Regression or Forecasting

"Constructing and Interpreting a Prediction Interval In Exercises 21-30, construct the indicated prediction interval and interpret the results.
21. Proceeds Construct a 95% prediction interval for the proceeds from initial public offerings in Exercise 11 when the number of offerings is 200."