MATHEMATICS
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 F_{max calc}? What is the tabular value of F_{max} at alpha = .05? Do we reject H_{0} for Hartley’s test at alpha = .05 ?
[removed] | 2, 10.8, fail to reject H_{0} | |
[removed] | 3, 10.4, reject H_{0} | |
[removed] | 4, 13.7, fail to reject H_{0} | |
[removed] | 1.33, 8.38, fail to reject H_{0 } | |
[removed] | 16,13.7, reject H_{0} |
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 H_{0}? (alpha =.05)
Bottom Middle Top
9 4 8
14 7 13
7 6 18
10 11 12
11
[removed] | 1.309, .5714, reject H_{0} | |
[removed] | 1.309, 2.74, fail to reject H_{0} | |
[removed] | 2.357, 2.74, fail to reject H_{0} | |
[removed] | 2.94, 2.74, reject H_{0} | |
[removed] | 2.74 , 1.309 reject H_{0} |
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 n_{T} and the number of populations is k, the mean square within treatments is
[removed] | SSE/(n_{T} – k) | |
[removed] | SSTR/(n_{T} – 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 (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_{0} equals
[removed] | 1 | |
[removed] | -1 | |
[removed] | 2 | |
[removed] | -2 |
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 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 (x^{2}) = 104
Sum (y) = 40
Sum (y^{2}) = 178
Sum (x)(y) = 134
n=10
Refer to Exhibit 14-1. Interpret the slope (b_{1})
[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 Variable |
Independent Variable |
5 | 15 |
7 | 12 |
9 | 10 |
11 | 7 |
Refer to Exhibit 14-2. The least squares estimate of b_{1} 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
s_{b1} = 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
Sx^{2} = 385
Sy^{2 }= 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
s_{b1} = 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 |