A random sample of 19 companies from the Forbes 500 list was selected, and the r

Question

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 Profitsi = + Salesi + i where the deviations i 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 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) The slope of the least-squares regression line is (approximately)? a. 0.09.       b. 0.0075.     c. –176.64.       d.61.16.

Explanation / Answer

The estimated regression model is

Profitsi = -176.644+0.092498 Salesi

to predict the profits (in hundreds of thousands of dollars) for companies that had sales (in hundreds of thousands of dollars) of 500 is

Profitsi = -176.644+0.092498 *500 = -130.395

The slope of the least-squares regression line is 0.09

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.