Use the following information for questions:
A sample of 19 female bears was measured for chest girth (y) and neck girth (x), both in inches. The least squares regression equation relating the two variables is $\hat{y}$= 5.32 + 1.53 x. The standard deviation of the regression is s = 3.692.
-What is a 95% prediction interval for the chest girth of a bear with a neck girth of 18 inches? The standard error of the fit, s.e.(fit), = 0.860
A) (24.9, 40.9)
B) (28.1, 43.7)
C) (31.0, 34.7)
D) None of the above

Question

Use the following information for questions:
 A sample of 19 female bears was measured for chest girth (y) and neck girth (x), both in inches. The least squares regression equation relating the two variables is $\hat{y}$= 5.32 + 1.53 x. The standard deviation of the regression is s = 3.692.
-What is a 95% prediction interval for the chest girth of a bear with a neck girth of 18 inches? The standard error of the fit, s.e.(fit), = 0.860
A) (24.9, 40.9)
B) (28.1, 43.7)
C) (31.0, 34.7)
D) None of the above

Quizplus · Accepted Answer

The 95% prediction interval is given by:$\hat{y} \pm t_{n-2, 0.025} \times s.e.(fit) \times \sqrt{1 + \frac{1}{n} + \frac{(x - \bar{x})^2}{\sum(x_i - \bar{x})^2}}$where:$\hat{y}$ is the predicted value of the dependent variable$t_{n-2, 0.025}$ is the t-value with n-2 degrees of freedom and a significance level of 0.025$s.e.(fit)$ is the standard error of the fit$n$ is the sample size$x$ is the value of the independent variable for which we are making the prediction$\bar{x}$ is the mean of the independent variable$\sum(x_i - \bar{x})^2$ is the sum of squared deviations of the independent variable from its meanPlugging in the given values, we get:$\hat{y} \pm t_{17, 0.025} \times 0.860 \times \sqrt{1 + \frac{1}{19} + \frac{(18 - 14.84)^2}{128.56}}$$\hat{y} \pm 2.110 \times 0.860 \times \sqrt{1.053 + 0.053 + 0.694}$$\hat{y} \pm 2.110 \times 0.860 \times 1.347$$\hat{y} \pm 1.839$Therefore, the 95% prediction interval is (24.9, 40.9).

Use the Following Information for Questions: a Sample of 19

Use the Following Information for Questions:
a Sample of 19