Refer to the simple linear regression of number of employees y and age x for fast-growing firms, Exercises 9.21,9.29, and 9.41. The SAS printout of the analysis is reproduced on page 526.
a. A 95% prediction interval for y when x = 10 is shown at the bottom of the printout. Interpret this interval.
b. How would the width of a 95% confidence interval for E(y) when x = 10 compare to the interval, part a?
c. Would you recommend using the model to predict the number of employees at a firm that has been in business two years'? Explain.
Exercises 9.41
Refer to Exercises 9.21 and 9.29 (p. 487,493). The SAS simple linear regression printout relating number of employees y to age of a fast-growing firm x is reproduced above.
a. Test to determine whether y is positively linearly related to x. Use α = .01.
b. Construct a 99% confidence interval for ß1. Practically interpret the result.
Exercises 9.21
The downsizing and restructuring that took place in corporate America during the 1990s encouraged both laid off middle managers and recent graduates of business schools to become entrepreneurs and start their own businesses. Assuming a business start-up does well, how fast will it grow? Can it expect to need 10 employees in three years or 50 or 100? To answer these questions, a random sample of 12 firms were drawn from the Inc. Magazine's "1996 Ranking of the Fastest-Growing Private Companies in America." The age (in years since 1995), x, and number of employees (in 1995), y, of each firm are
recorded in the table at left. SAS was used to conduct a simple linear regression analysis for the model. E(y) = ßo + ß1x. The printout is shown below.
a. Plot the data in a scattergram. Does the number of employees at a fast-growing firm appear to increase linearly as the firm's age increases?
b. Find the estimates of ß0 and ß1 in the SAS printout. Interpret their values.
Exercises 9.29
Refer to the simple linear regression relating number of employees y to age x of a fast-growing firm, Exercise 9.21 (p. 487).The SAS printout is reproduced on the next page.
a. Find SSE, s2, and s on the printout.
b. Interpret the value of s
