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 (x2) = 104
Sum (y) = 40
Sum (y2) = 178
Sum (x)(y) = 134
n=10
Refer to Exhibit 14-1. The least squares estimate of b1 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 |
H0: m1=m2=m3=m4 |
|
SSE = 8,000 |
Ha: at least one mean is different |
|
nT = 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 |
H0: m1=m2=m3=m4 |
|
SSE = 8,000 |
Ha: at least one mean is different |
|
nT = 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 |
H0: m1=m2=m3=m4 |
|
SSE = 8,000 |
Ha: at least one mean is different |
|
nT = 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 |
H0: m1=m2=m3=m4 |
|
SSE = 8,000 |
Ha: at least one mean is different |
|
nT = 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 |
15. Exhibit 14-1
A regression analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x).
n = 10
Sx = 55
Sy = 55
Sx2 = 385
Sy2 = 385
Sxy = 220
Refer to Exhibit 14-1. The point estimate of y when x = 20 is
|
[removed] |
0 |
|
|
[removed] |
31 |
|
|
[removed] |
9 |
|
|
[removed] |
-9 |
Coefficient of determination = +1
16. Exhibit 14-1A regression analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x).
Sum (x) = 30
Sum (x2) = 104
Sum (y) = 40
Sum (y2) = 178
Sum (x)(y) = 134
n=10
Refer to Exhibit 14-1. Interpret the y-intercept.
|
[removed] |
The estimated value of x is 1 if y is 0. |
|
|
[removed] |
The estimated value of y is 1 if x is 0. |
|
|
[removed] |
The estimated increase in y is 1 for each additional unit of x. |
|
|
[removed] |
The estimated increase in x is 1 for each addition unit of y. |
17. You are given the following information about y and x.
|
y |
x |
|
Dependent |
Independent |
|
5 |
15 |
|
7 |
12 |
|
9 |
10 |
|
11 |
7 |
Refer to Exhibit 14-2. The least squares estimate of b0 equals
|
[removed] |
-7.647 |
|
|
[removed] |
-1.3 |
|
|
[removed] |
21.4 |
|
|
[removed] |
16.41176 |
18. Exhibit 14-2You are given the following information about y and x.
|
y |
x |
|
Dependent |
Independent |
|
5 |
15 |
|
7 |
12 |
|
9 |
10 |
|
11 |
7 |
Refer to Exhibit 14-2. The coefficient of determination equals
|
[removed] |
-0.99705 |
|
|
[removed] |
-0.9941 |
|
|
[removed] |
0.9941 |
|
|
[removed] |
0.99705 |
19. Exhibit 14-3
Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained.
y cap = 12 + 1.8 x
n = 17
SSR = 225
SSE = 75
sb1 = 0.2683
Refer to Exhibit 14-3. Based on the above estimated regression equation, if advertising is $3,000, then the point estimate for sales (in dollars) is
|
[removed] |
$66,000 |
|
|
[removed] |
$5,412 |
|
|
[removed] |
$66 |
|
|
[removed] |
$17,400 |
20. Exhibit 14-3
Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained.
y cap = 12 + 1.8 x
n = 17
SSR = 225 SSE = 75
sb1 = 0.2683
Refer to Exhibit 14-3. The t statistic for testing the significance of the slope is
|
[removed] |
1.80 |
|
|
[removed] |
1.96 |
|
|
[removed] |
6.709 |
|
|
[removed] |
0.555 |
21. The following results were obtained as a part of simple regression analysis:
r2 = .9162
F statistic from the Ftable = 3.59
Calculated value of F from the ANOVA table = 81.87
alpha = .05
p-value = .0000
The null hypothesis of no relationship between the dependent variable and the independent variable
|
[removed] |
is rejected |
|
|
[removed] |
cannot be tested with the given information |
|
|
[removed] |
is not rejected |
|
|
[removed] |
is not an appropriate null hypothesis for this situation |
22. The degrees of freedom error (within group variation) of a completely randomized design (one way ANOVA) test with four groups (treatments) and 15 observations per each group is:
|
[removed] |
3 |
|
|
[removed] |
56 |
|
|
[removed] |
59 |
|
|
[removed] |
14 |
|
|
[removed] |
4 |
23. When computing an individual confidence interval using t statistic for comparing more than two means and if we do all possible pairwise comparisons of means, the experimentwise error rate will be
|
[removed] |
equal to alpha |
|
|
[removed] |
less than alpha |
|
|
[removed] |
greater than alpha |
|
|
[removed] |
may be less than or greater than alpha |
24. After analyzing a data set using one-way analysis of variance, the same data is analyzed using a two factor, full factorial design ANOVA model with two observations per cell. The F statistic for the treatment in the one way ANOVA is ______________________ smaller than the F statistic for treatment in the two-factor full factorial design ANOVA model.
|
[removed] |
always |
|
|
[removed] |
sometimes |
|
|
[removed] |
never |
|
|
[removed] |
25. In a latin Squares design ANOVA with 6 treatments, total degrres of freedom and degrees of freedom error are:
|
[removed] |
36,21 |
|
|
[removed] |
15,10 |
|
|
[removed] |
35,20 |
|
|
[removed] |
35,5 |
|
|
[removed] |
36,6 |
26. Which of the following is not a major assumption of the simple regression model:
|
[removed] |
Independence of error terms |
|
|
[removed] |
Nominal data |
|
|
[removed] |
Normal distribution of the variables |
|
|
[removed] |
Equal (constant) variances |
27. A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple regression analysis on the data below.
City Price, ($) Sales
River Falls 1.20 100
Hudson 1.60 90
Ellsworth 1.80 90
Prescott 2.00 40
Rock Elm 2.40 38
Stillwater 3.00 32
Using least squares regression, what is the estimated slope parameter for the candy bar price and sales data?
|
[removed] |
-40.00 |
|
|
[removed] |
-48.193 |
|
|
[removed] |
-43.40 |
|
|
[removed] |
-3.81 |
|
|
[removed] |
-28.07 |
28. A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple regression analysis on the data below.
City Price, ($) Sales
River Falls 1.20 100
Hudson 1.60 90
Ellsworth 1.80 90
Prescott 2.00 40
Rock Elm 2.40 38
Stillwater 3.00 32
What proportion of the variation in candy’s sales price is explained by the simple linear regression equation?
|
[removed] |
76.6% |
|
|
[removed] |
67.2% |
|
|
[removed] |
67.4% |
|
|
[removed] |
78.0% |
|
|
[removed] |
72.9% |
29. A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple regression analysis on the data below.
City Price, ($) Sales
River Falls 1.20 100
Hudson 1.60 90
Ellsworth 1.80 90
Prescott 2.00 40
Rock Elm 2.40 38
Stillwater 3.00 32
What is the standard error of estimate?
|
[removed] |
20.09 |
|
|
[removed] |
15.29 |
|
|
[removed] |
16.96 |
|
|
[removed] |
19.16 |
|
|
[removed] |
22.31 |
30. A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple regression analysis on the data below.
City Price, ($) Sales
River Falls 1.20 100
Hudson 1.80 80
Ellsworth 1.80 100
Prescott 2.00 40
Rock Elm 2.00 38
Stillwater 3.00 32
What is the F-tab value for the significance test for the linear model? (alpha=0.05)
|
[removed] |
199.50 |
|
|
[removed] |
4.89 |
|
|
[removed] |
4.54 |
|
|
[removed] |
7.71 |
|
|
[removed] |
10.13 |
31. In a one-way analysis of variance problem, there are four treatments and six observations in each treatment. The sample variances of of the four treatments are as follows: 9, 12, 3, 6.What is value of Fmax calc? What is the tabular value of Fmax at alpha = .05? Do we reject H0 for Hartley’s test at alpha = .05 ?
|
[removed] |
2, 10.8, fail to reject H0 |
|
|
[removed] |
3, 10.4, reject H0 |
|
|
[removed] |
4, 13.7, fail to reject H0 |
|
|
[removed] |
1.33, 8.38, fail to reject H0 |
|
|
[removed] |
16,13.7, reject H0 |
32. Following partially completed two way ANOVA table is given for a two factor experiment with 4 treatments three blocks and total of 36 observations:
Source SS df MS F
Treatment 3
Block 4
Interaction 1
Error
Total
In this experiment there are _________ replications per cell. The degrees of freedom are:: ____________ for treatments, ____________ for blocks, ________________ error, and ___________ for interaction.
|
[removed] |
3, 3, 2, 24, 6 |
|
|
[removed] |
2, 3, 2, 12, 6 |
|
|
[removed] |
2, 4, 3, 15, 12 |
|
|
[removed] |
3, 3, 2, 25, 6 |
|
|
[removed] |
3, 6, 4, 2 |
33. Using the summary information given below for shelf height in advertising, if Tukey’s hypothesis test is performed between bottom and middle shelves, where MSE = 10.5, what is the t calculated statistics value, critical value of Tukey statistic,do we reject H0? (alpha =.05)
Bottom Middle Top
9 4 8
14 7 13
7 6 18
10 11 12
11
|
[removed] |
1.309, .5714, reject H0 |
|
|
[removed] |
1.309, 2.74, fail to reject H0 |
|
|
[removed] |
2.357, 2.74, fail to reject H0 |
|
|
[removed] |
2.94, 2.74, reject H0 |
|
|
[removed] |
2.74 , 1.309 reject H0 |
34. An experiment was conducted on a certain metal to determine if strength of the metal is a function of the time it is heated.Linear regression equation is:Y hat = 1 + 1X. Sum of the squared (X- X bar) values is 14, MSE = .5, X bar = 3, and there are a total of 10 observations (X (time), Y (strength) pairs). Determine the 95% confidence interval for the strength, if the metal is heated for 2.5 minutes.
|
[removed] |
3.104 to 3.896 |
|
|
[removed] |
3.05 to 3.95 |
|
|
[removed] |
2.94 to 4.06 |
|
|
[removed] |
1.791 to 5.209 |
|
|
[removed] |
2.286 to 4.714 |
35. An experiment was conducted on a certain metal to determine if strength of the metal is a function of the time it is heated.Y hat = 1+1X. Sum of the squared (X -X bar) values is 14, MSE = .5, X bar = 3, and there are a total of 10 observations (X (time), Y (strength) pairs). Determine the 99% prediction interval for strength, if metal is heated for 2.5 minutes.
|
[removed] |
1.7909 to 5.209 |
|
|
[removed] |
.992 to 6.008 |
|
|
[removed] |
2.281 to 4.719 |
|
|
[removed] |
1.726 to 5.724 |
|
|
[removed] |
2.93 to 4.07 |
NEW SUBMISSION
2. You wish to add a categorical explanatory variable with two categories to a regression model. How many dummy variables are required to represent the categories?
|
[removed] |
one |
|
|
[removed] |
two |
|
|
[removed] |
three |
|
|
[removed] |
four |
3. The F ratio in a completely randomized ANOVA is the ratio of
|
[removed] |
MSTR/MSE |
|
|
[removed] |
MST/MSE |
|
|
[removed] |
MSE/MSTR |
|
|
[removed] |
MSE/MST |
4. In an analysis of variance where the total sample size for the experiment is nT and the number of populations is k, the mean square within treatments is
|
[removed] |
SSE/(nT – k) |
|
|
[removed] |
SSTR/(nT – k) |
|
|
[removed] |
SSE/(k – 1) |
|
|
[removed] |
SSE/k |
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 (x2) = 104
Sum (y) = 40
Sum (y2) = 178
Sum (x)(y) = 134
n=10
Refer to Exhibit 14-1. The least squares estimate of b0 equals
|
[removed] |
1 |
|
|
[removed] |
-1 |
|
|
[removed] |
2 |
|
|
[removed] |
-2 |
8. Exhibit 13-1
|
SSTR = 6,750 |
H0: m1=m2=m3=m4 |
|
SSE = 8,000 |
Ha: at least one mean is different |
|
nT = 20 |
|
Refer to Exhibit 13-1. The mean square between treatments (MSTR) equals
|
[removed] |
400 |
|
|
[removed] |
500 |
|
|
[removed] |
1,687.5 |
|
|
[removed] |
2,250 |
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 mean square within treatments (MSE) equals
|
[removed] |
1.872 |
|
|
[removed] |
5.86 |
|
|
[removed] |
34 |
|
|
[removed] |
36 |
13. A regression analysis between sales (y in $1000) and advertising (x in dollars) resulted in the following equation
y cap = 50,000 + 6 x
The above equation implies that an
|
[removed] |
increase of $6 in advertising is associated with an increase of $6,000 in sales |
|
|
[removed] |
increase of $1 in advertising is associated with an increase of $6 in sales |
|
|
[removed] |
increase of $1 in advertising is associated with an increase of $56,000 in sales |
|
|
[removed] |
increase of $1 in advertising is associated with an increase of $6,000 in sales |
15. Exhibit 14-1A regression analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x).
Sum (x) = 30
Sum (x2) = 104
Sum (y) = 40
Sum (y2) = 178
Sum (x)(y) = 134
n=10
Refer to Exhibit 14-1. Interpret the slope (b1)
|
[removed] |
The value of y increases by 1 for each additional x value. |
|
|
[removed] |
The value of x increases by 1 for each additional y value. |
|
|
[removed] |
The value of y is 1 if x is 0. |
|
|
[removed] |
The value of x is 1 if y is 0. |
17. You are given the following information about y and x.
|
y |
x |
|
Dependent |
Independent |
|
5 |
15 |
|
7 |
12 |
|
9 |
10 |
|
11 |
7 |
Refer to Exhibit 14-2. The least squares estimate of b1 equals
|
[removed] |
-0.7647 |
|
|
[removed] |
-0.13 |
|
|
[removed] |
21.4 |
|
|
[removed] |
16.412 |
19. Exhibit 14-3
Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained.
y cap = 12 + 1.8 x
n = 17
SSR = 225
SSE = 75
sb1 = 0.2683
Refer to Exhibit 14-3. The F statistic computed from the above data is
|
[removed] |
3 |
|
|
[removed] |
45 |
|
|
[removed] |
48 |
|
|
[removed] |
Not enough information is given to answer this question. |
20. In an analysis of variance problem if SST = 120 and SSTR = 80, then SSE is
|
[removed] |
200 |
|
|
[removed] |
40 |
|
|
[removed] |
80 |
|
|
[removed] |
120 |
21. A least squares regression line
|
[removed] |
may be used to predict a value of y if the corresponding x value is given |
|
|
[removed] |
implies a cause-effect relationship between x and y |
|
|
[removed] |
can only be determined if a good linear relationship exists between x and y |
|
|
[removed] |
All of these answers are correct. |
22. Exhibit 14-1
A regression analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x).
n = 10
Sx = 55
Sy = 55
Sx2 = 385
Sy2 = 385
Sxy = 220
Refer to Exhibit 14-1. The coefficient of determination equals
|
[removed] |
0 |
|
|
[removed] |
-1 |
|
|
[removed] |
+1 |
|
|
[removed] |
-0.5 |
23. Exhibit 14-3
Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained.
y cap = 12 + 1.8 x
n = 17
SSR = 225
SSE = 75
sb1 = 0.2683
Refer to Exhibit 14-3. Using a = 0.05, the critical t value for testing the significance of the slope is
|
[removed] |
1.753 |
|
|
[removed] |
2.131 |
|
|
[removed] |
1.746 |
|
|
[removed] |
2.120 |
