Suppose we wish to predict the profits (in hundreds of thousands of dollars) for
ID: 3263550 • Letter: S
Question
Suppose we wish to predict the profits (in hundreds of thousands of dollars) for companies that had sales (in hundreds of thousands of dollars) of 500. We use statistical software to do the prediction and obtain the following output.
Sales Predict Stdev. mean predict 95% C.I. 95% P.I.
500 –130.4 59.3 (–248.5, –12.3) (–1066.4, 805.6)
A random sample of 19 companies from the Forbes 500 list was selected, and the relationship between sales (in hundreds of thousands of dollars) and profits (in hundreds of thousands of dollars) was investigated by regression. The following simple linear regression model was used
Profits = + (Sales)
where the deviations were assumed to be independent and Normally distributed, with mean 0 and standard deviation . This model was fit to the data using the method of least squares. The following results were obtained from statistical software.
r2 = 0.662 s = 466.2
Parameter Parameter est. Std. err. of parameter est.
–176.644 61.16
0.092498 0.0075
Suppose we wish to predict the profits (in hundreds of thousands of dollars) for a company that had sales (in hundreds of thousands of dollars) of 500. A 95% interval for this prediction is
a) –1066.4 to 805.6. b) –248.5 to –12.3. c) –189.7 to –71.1. d) 400.7 to 559.3.
Explanation / Answer
from the given data, 95% intervalpredicted when the sales had $500 profit is
option c
is the right answer
i.e; 95% ci = (-28405 , -12.3)