A multiple linear regression model based on a sample of 23 months is developed t
ID: 3170265 • Letter: A
Question
A multiple linear regression model based on a sample of 23 months is developed to predict distribution cost for a warehouse based on the sales and number of orders. The SSR is 25,127.13 and the SSE is 435.19. Complete parts (a) through (d) below.
Calculate the test statistic. FSTAT=________________ (Round to two decimal places as needed.)
Determine the p-value. The p-value is _________________ (Round to four decimal places as needed.)
State the conclusion. Since the p-value is (1) __________________than the level of significance, (2)_______________________ the null hypothesis. There is (3) ____________________ evidence to conclude there is a linear relationship.
b. Interpret the meaning of the p-value. Choose the correct answer below.
A.The p-value is the probability of getting an overall test statistic equal to or less than the sample result, assuming there is no linear relationship between the dependent variable and the independent variables.
B.The p-value is the probability of getting an overall test statistic equal to or greater than the sample result, assuming there is no linear relationship between the dependent variable and the independent variables.
C.The p-value is the probability that there is a linear relationship between the two independent variables.
D.The p-value is the probability that there is a linear relationship between the dependent variable and at least one of the independent variables.
c. Compute the coefficient of multiple determination, r2 ,and interpret its meaning.
r2=____________________(Round to four decimal places as needed)
Interpret the meaning of r2.
The coefficient of multiple determination indicates that _________________% of the variation in (4)_________________can be explained by the variation in (5) ______________
(Round to two decimal places as needed)
d. Compute the adjusted r2
r2adj=______________________ (Round to four decimal places as needed.)
(1)____greater _____less
(2) _____do not reject _____reject
(3) _____sufficient _____insufficient
(4) _____sales and numbers of orders _____numbers of orders _____sales _____distribution cost
(5) _____sales _____number of orders _____distribution cost ______sales and number of orders
Explanation / Answer
Result:
A multiple linear regression model based on a sample of 23 months is developed to predict distribution cost for a warehouse based on the sales and number of orders. The SSR is 25,127.13 and the SSE is 435.19. Complete parts (a) through (d) below.
DF
SS
MSS
F
Regression
2
25127.13
12563.57
577.383
Error
20
435.19
21.7595
Total
22
25562.32
Calculate the test statistic. FSTAT= 577.38 (Round to two decimal places as needed.)
Determine the p-value. The p-value is 0.0000 (Round to four decimal places as needed.)
State the conclusion. Since the p-value is (1) less than the level of significance, (2) reject the null hypothesis. There is (3) sufficient evidence to conclude there is a linear relationship.
b. Interpret the meaning of the p-value. Choose the correct answer below.
A.The p-value is the probability of getting an overall test statistic equal to or less than the sample result, assuming there is no linear relationship between the dependent variable and the independent variables.
B.The p-value is the probability of getting an overall test statistic equal to or greater than the sample result, assuming there is no linear relationship between the dependent variable and the independent variables.
C.The p-value is the probability that there is a linear relationship between the two independent variables.
D.The p-value is the probability that there is a linear relationship between the dependent variable and at least one of the independent variables.
c. Compute the coefficient of multiple determination, r2 ,and interpret its meaning.
r2=0.9830 (Round to four decimal places as needed)
Interpret the meaning of r2.
The coefficient of multiple determination indicates that 98.30 % of the variation in (4) distribution cost can be explained by the variation in (5) sales and number of orders
(Round to two decimal places as needed)
d. Compute the adjusted r2
r2adj=0.9813 (Round to four decimal places as needed.)
DF
SS
MSS
F
Regression
2
25127.13
12563.57
577.383
Error
20
435.19
21.7595
Total
22
25562.32
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