Use the following to answer the following 3 questions: A random sample of 79 com
ID: 3251751 • Letter: U
Question
Use the following to answer the following 3 questions: 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 simple linear regression model was used
Profits_i = beta0 + beta1 (Sales)_i + _i
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:
R^2 = .662 s = 466.2
variable Parameter Estimate SE of Parameter
Constant -176.644 61.16
Sales .092498 .0075
Suppose the researchers test the hypotheses:
H0: beta1 = 0 vs. Ha: beta1 > 0
The P-value of the test is:
a) greater than 0.10.
b) between 0.10 and 0.05.
c) between 0.05 and 0.01.
d) less than 0.01.
Is there strong evidence (and if so, why) of a straight line relationship between sales and profits?
a) Yes, because the slope of the least-squares line is positive.
b) Yes, because the P-value for testing if the slope is 0 is quite small.
c) No, because the value of the square of the correlation is relatively small.
d) It is impossible to say because we are not given the actual value of the correlation.
a) greater than 0.10.
b) between 0.10 and 0.05.
c) between 0.05 and 0.01.
d) less than 0.01.
Is there strong evidence (and if so, why) of a straight line relationship between sales and profits?
a) Yes, because the slope of the least-squares line is positive.
b) Yes, because the P-value for testing if the slope is 0 is quite small.
c) No, because the value of the square of the correlation is relatively small.
d) It is impossible to say because we are not given the actual value of the correlation.
Explanation / Answer
Answer to the questions:
The p-value of the test is :?
The t value is .092498/.0075 = 12.33
The p value from the ttables is less than .01
d) is the right answer
2nd Ques)
b is the right answer) Yes, because the p-value for testing if the slope is 0, is quite small
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