A random sample of 79 companies from the Forbes 500 list (which actually consist
ID: 3157955 • Letter: A
Question
A random sample of 79 companies from the Forbes 500 list (which actually consists of nearly 800 companies) 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 results were obtained from statistical software.
R2 = 0.662
s = 466.2
Variable
Parameter estimate
Standard error
Constant
–176.644
61.16
Sales
0.092498
0.0075
Suppose the researchers conducting this study wish to estimate the profits (in hundreds of thousands of dollars) for companies that had sales (in hundreds of thousands of dollars) of 500. The following results were obtained from statistical software.
Sales
Predicted profit
Standard error
95.0% C.I.
95.0% P.I.
500
–130.4
59.3
(–248.5, –12.3)
(–1066.4, 805.6)
If the researchers wish to estimate the profits for a particular company that had sales of 500, what would be a 95% prediction interval for the profits?
500 ± 59.3
(–248.5, –12.3)
(–1066.4, 805.6)
–130.4 ± 59.3
What is an approximate 90% confidence interval for the slope 1?
0.09 ± 0.0075
–0.09 ± 0.0125
0.09 ± 0.0125
–0.09 ± 0.0075
What are the degrees of freedom for SSE, the error sum of squares?
77
78
2
79
What is the value of the SST, the total sum of squares?
32,809,212
49,543,448
16,734,234
16,074,978
What is the value of the F statistic for testing the hypotheses H0: 1 = 0 versus
Ha: 1 0?
77
150.97
1.96
217,328
A random sample of 79 companies from the Forbes 500 list (which actually consists of nearly 800 companies) 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 results were obtained from statistical software.
R2 = 0.662
s = 466.2
Variable
Parameter estimate
Standard error
Constant
–176.644
61.16
Sales
0.092498
0.0075
Suppose the researchers conducting this study wish to estimate the profits (in hundreds of thousands of dollars) for companies that had sales (in hundreds of thousands of dollars) of 500. The following results were obtained from statistical software.
Sales
Predicted profit
Standard error
95.0% C.I.
95.0% P.I.
500
–130.4
59.3
(–248.5, –12.3)
(–1066.4, 805.6)
If the researchers wish to estimate the profits for a particular company that had sales of 500, what would be a 95% prediction interval for the profits?
500 ± 59.3
(–248.5, –12.3)
(–1066.4, 805.6)
–130.4 ± 59.3
What is an approximate 90% confidence interval for the slope 1?
0.09 ± 0.0075
–0.09 ± 0.0125
0.09 ± 0.0125
–0.09 ± 0.0075
Explanation / Answer
a) -130+/- 59.3
b) As in the given Sales data coeffiecient, the answer is Param estimate +/- standard error. t can be calculted as 1.66 for n-2 and apha/2 i.e. 77, 0.,05 from t tables
Therefore, 0.09 ± 0.0075 *1.66(c) t
c) Df = N-k-1, N=number of Obs, k= No. of Variables. Since there is just 1 Variable-sales- we have Df= 79-1-1=77
d) SSt =
e) F = 150.92, therefore a)
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