Suppose We Wish to Predict the Profits (In Hundreds of Thousands

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 units. We use statistical software to do the prediction and obtain the following output. 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 = $\alpha$ + $\beta$ (sales) , where the deviations were assumed to be independent and Normally distributed, with mean 0 and standard deviation $\sigma$ . 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 A 95% confidence interval for the average profit of companies with 500 units of sales 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.