Question

"Constructing and Interpreting a Prediction Interval In Exercises 21-30, construct the indicated prediction interval and interpret the results.
30. New Vehicle Sales Construct a 99% prediction interval for new vehicle sales for Honda in Exercise 20 when the number of new vehicles sold by Toyota is 2159 thousand."

Accepted Answer

Identify the regression equation from Exercise 20, which relates the number of new vehicles sold by Toyota (independent variable, x) to the number of new vehicles sold by Honda (dependent variable, y). This equation typically has the form: \hat{y} = $$b_0 + b_1x$$, where $$b_0 is $$the intercept and $$b_1 is $$the slope. Calculate the predicted value \hat{y} for Honda vehicle sales when Toyota sales are 2159 thousand by substituting x = 2159 into the regression equation. Determine the standard error of the prediction, which accounts for both the variability of the estimate of the mean response and the variability of individual observations. The formula for the standard error of prediction at a specific x is: SE_{pred} = s \sqrt{1 + \frac{1}{n} + \frac{(x - \bar{x}$$)^2$$}{\sum (x_i - \bar{x}$$)^2$$}}, where s is the standard error of the estimate, n is the sample size, \bar{x} is the mean of the x values, and x_i are the observed x values. Find the critical t-value for a 99% prediction interval with degrees of freedom equal to n - 2. This value comes from the t-distribution table and reflects the desired confidence level. Construct the 99% prediction interval using the formula: \hat{y} \pm t_{\alpha/2, n-2} 	imes SE_{pred}. Interpret this interval as the range in which we expect the actual number of Honda vehicle sales to fall with 99% confidence when Toyota sales are 2159 thousand.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Prediction Interval

Confidence Level

Regression and Using Predictor Variables