MATHEMATICS
fRefer to Exhibit 13-3. The mean square between treatments (MSTR) equals1. In a simple linear regression problem with 10 observations (sample size = n = 10). There are 6 unique observations. ANOVA table is gathered to see if simple regression equation is significant. Another ANOVA test is conducted to see if linear relationship is adequate. For these two problems degrees of freedom total, regression, error, lack of fit, pure error are:
[removed] | 10, 1, 9, 4, 5 | |
[removed] | 9, 1, 8, 4, 4 | |
[removed] | 9, 1, 8, 3, 5 | |
[removed] | 9, 1, 8, 5, 3 |
2. You wish to add a categorical explanatory variable with three categories to a regression model. How many dummy variables are required to represent the categories?
[removed] | one | |
[removed] | two | |
[removed] | three | |
[removed] | four |
3.
3. 3 categories and 10 observations per category, SSE = 399.6, MSE =
a. 133.2
b. 13.32
c. 14.8
d. 30.0
4. The critical F value with 6 numerator and 60 denominator degrees of freedom at a = .05 is
[removed] | 3.74 | |
[removed] | 2.25 | |
[removed] | 2.37 | |
[removed] | 1.96 |
5. Exhibit 14-1A regression analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x).
Sum (x) = 30
Sum (x^{2}) = 104
Sum (y) = 40
Sum (y^{2}) = 178
Sum (x)(y) = 134
n=10
Refer to Exhibit 14-1. The least squares estimate of b_{1} equals
[removed] | 1 | |
[removed] | -1 | |
[removed] | 2 | |
[removed] | -2 |
6. In a regression analysis if SST=4500 and SSE=1575, then the coefficient of determination is
[removed] | 0.35 | |
[removed] | 0.65 | |
[removed] | 2.85 | |
[removed] | 0.45 |
7. Exhibit 13-1
SSTR = 6,750 | H_{0}: m_{1}=m_{2}=m_{3}=m_{4} |
SSE = 8,000 | H_{a}: at least one mean is different |
n_{T} = 20 | |
Refer to Exhibit 13-1. The mean square within treatments (MSE) equals
[removed] | 400 | |
[removed] | 500 | |
[removed] | 1,687.5 | |
[removed] | 2,250 |
8. Exhibit 13-1
SSTR = 6,750 | H_{0}: m_{1}=m_{2}=m_{3}=m_{4} |
SSE = 8,000 | H_{a}: at least one mean is different |
n_{T} = 20 | |
Refer to Exhibit 13-1. The null hypothesis is to be tested at the 5% level of significance. The critical value from the table is
[removed] | 2.87 | |
[removed] | 3.24 | |
[removed] | 4.08 | |
[removed] | 8.7 |
9. Exhibit 13-3
To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below.
Treatment | Observation | |||
A | 20 | 30 | 25 | 33 |
B | 22 | 26 | 20 | 28 |
C | 40 | 30 | 28 | 22 |
Refer to Exhibit 13-3. The test statistic to test the null hypothesis equals
[removed] | 0.944 | |
[removed] | 1.059 | |
[removed] | 3.13 | |
[removed] | 19.231 |
10. Exhibit 13-3
To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below.
Treatment | Observation | |||
A | 20 | 30 | 25 | 33 |
B | 22 | 26 | 20 | 28 |
C | 40 | 30 | 28 | 22 |
Refer to Exhibit 13-3. The mean square between treatments (MSTR) equals
[removed] | 1.872 | |
[removed] | 5.86 | |
[removed] | 34 | |
[removed] | 36 |
11. Exhibit 13-1
SSTR = 6,750 | H_{0}: m_{1}=m_{2}=m_{3}=m_{4} |
SSE = 8,000 | H_{a}: at least one mean is different |
n_{T} = 20 | |
Refer to Exhibit 13-1. The test statistic to test the null hypothesis equals
[removed] | 0.22 | |
[removed] | 0.84 | |
[removed] | 4.22 | |
[removed] | 4.5 |
12. Exhibit 13-1
SSTR = 6,750 | H_{0}: m_{1}=m_{2}=m_{3}=m_{4} |
SSE = 8,000 | H_{a}: at least one mean is different |
n_{T} = 20 | |
Refer to Exhibit 13-1. The null hypothesis
[removed] | should be rejected | |
[removed] | should not be rejected | |
[removed] | was designed incorrectly | |
[removed] | None of these alternatives is correct. |
13. In regression analysis if the dependent variable is measured in dollars, the independent variable
[removed] | must also be in dollars | |
[removed] | must be in some unit of currency | |
[removed] | can be any units | |
[removed] | can not be in dollars |
14. A regression analysis between demand (y in 1000 units) and price (x in dollars) resulted in the following equation
y cap = 9 – 3x
The above equation implies that if the price is increased by $1, the demand is expected to
[removed] | increase by 6 units | |
[removed] | decrease by 3 units | |
[removed] | decrease by 6,000 units | |
[removed] | decrease by 3,000 units |