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Question
In a multiple regression analysis with N observations and k independent variables, the degrees of freedom for the residual error is given by (N - k).
Answer
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Related questions
Q:
BigShots, Inc. is a specialty e-tailer that operates 87 catalog Web sites on the Internet. Kevin Conn, Sales Director, feels that the style (color scheme, graphics, fonts, etc.) of a Web site may affect its sales. He chooses three levels of design style (neon, old world and sophisticated) and randomly assigns six catalog Web sites to each design style. In Kevin's experiment "style" is _______.a) the dependent variableb) a treatment variablec) a concomitant variabled) a blocking variablee) a response variable
Q:
While reviewing staffing plans for a new pilot plant, Colin Chenaux, VP of Operations at Clovis Chemicals, Inc., designed an experiment to test the effects of "supervisor's style" and "training method" on the productivity of operators. The treatment levels were: (1) authoritarian, and participatory for supervisor's style, and (2) technical manuals, training films, and multimedia for training method. Three qualified applicants were randomly selected and assigned to each of the six cells. In Colin's experiment, "operator productivity" is _____________.
a) a concomitant variable
b) a treatment variable
c) the dependent variable
d) a blocking variable
e) a constant
Q:
Data from a randomized block design are shown in the following table. Treatment Levels 1
2
3
4 Block 1
8
5
10
7 Block 2
6
6
9
5 Block 3
7
8
8
9 The Error Sum of Squares (SSE) is ________.
a) 4.67
b) 12
c) 2.33
d) 28.67
e) 11
Q:
Cindy Ho, VP of Finance at Discrete Components, Inc. (DCI), theorizes that the discount level offered to credit customers affects the average collection period on credit sales. Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%). First, she classified DCI's credit customers into three categories by total assets (small, medium, and large). Then, she randomly assigned four customers from each category to a sales discount rate. In Cindy's experiment "sales discount rate" is ________.
a) a surrogate variable
b) the dependent variable
c) a blocking variable
d) a treatment variable
e) a constant
Q:
Cindy Ho, VP of Finance at Discrete Components, Inc. (DCI), theorizes that the discount level offered to credit customers affects the average collection period on credit sales. Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%). First, she classified DCI's credit customers into three categories by total assets (small, medium, and large). Then, she randomly assigned four customers from each category to a sales discount rate. In Cindy's experiment "average collection period" is ________.
a) a concomitant variable
b) the dependent variable
c) a treatment variable
d) a blocking variable
e) a constant
Q:
For the following ANOVA table, the critical value of the studentized range distribution using a= 0.05 is ______ Source of Variation
SS
df
MS
F Treatment
36.17
2
18.08
5.66 Error
28.75
9
3.19 Total
64.92
11 a) 1.86
b) 3.94
c) 9.17
d) 1.65
e) 1.79
Q:
Data from a completely randomized design are shown in the following table. Treatment Level 1
2
3 27
26
27 26
22
29 23
21
27 24
23
26 For a one-way ANOVA, the Error Sum of Squares (SSE) is ________.
a) 36.17
b) 28.75
c) 64.92
d) 18.03
e) 28.04
Q:
Data from a completely randomized design are shown in the following table. Treatment Level 1
2
3 27
26
27 26
22
29 23
21
27 24
23
26 For a one-way ANOVA, the Total Sum of Squares (SST) is ________.
a) 36.17
b) 28.75
c) 64.92
d) 18.03
e) 28.04
Q:
Cindy Ho, VP of Finance at Discrete Components, Inc. (DCI), theorizes that the discount level offered to credit customers affects the average collection period on credit sales. Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%) by randomly assigning five customers to each sales discount rate. An analysis of Cindy's data produced the following ANOVA table. Source of Variation
SS
df
MS
F Treatment
5.35
3
1.783333 Error
177.2
16
11.075 Total
182.55
19 Using a= 0.01, the appropriate decision is _________.
a) reject the null hypothesism1= m2= m3= m4
b) reject the null hypothesism1 m2 m3 m4
c) do not reject the null hypothesis m1= m2= m3= m4
d) do not reject the null hypothesis m1 m2 m3m4
e) do nothing
Q:
Cindy Ho, VP of Finance at Discrete Components, Inc. (DCI), theorizes that the discount level offered to credit customers affects the average collection period on credit sales. Accordingly, she has designed an experiment to test her theory using four sales discount rates (0%, 2%, 4%, and 6%) by randomly assigning five customers to each sales discount rate. In Cindy's experiment, "average collection period" is ________.
a) the dependent variable
b) a treatment variable
c) a blocking variable
d) a concomitant variable
e) a constant
Q:
BigShots, Inc. is a specialty e-tailer that operates 87 catalog Web sites on the Internet. Kevin Conn, Sales Director, feels that the style (color scheme, graphics, fonts, etc.) of a Web site may affect its sales. He chooses three levels of design style (neon, old world and sophisticated) and randomly assigns six catalog Web sites to each design style. Analysis of Kevin's data yielded the following ANOVA table. Source of Variation
SS
df
MS
F Between Groups
384.3333
2
192.1667 Within Groups
1359.667
15
90.64444 Total
1744
17 Using a= 0.05, the appropriate decision is _____________.
a) do not reject the null hypothesism1 = m2 = m3
b) do not reject the null hypothesism1 m2 m3
c) reject the null hypothesis m1 m2 m3
d) reject the null hypothesis m1 m2 m3
e) do nothing
Q:
BigShots, Inc. is a specialty e-tailer that operates 87 catalog Web sites on the Internet. Kevin Conn, Sales Director, feels that the style (color scheme, graphics, fonts, etc.) of a Web site may affect its sales. He chooses three levels of design style (neon, old world and sophisticated) and randomly assigns six catalog Web sites to each design style. Analysis of Kevin's data yielded the following ANOVA table. Source of Variation
SS
df
MS
F Between Groups
68102.33
2
34051.17 Within Groups
29177.67
15
1945.178 Total
97280
17 Using a= 0.05, the observed F value is _____________.
a) 0.5022
b) 0.1333
c) 1.9911
d) 17.5100
e) 22.4567
Q:
BigShots, Inc. is a specialty e-tailer that operates 87 catalog Web sites on the Internet. Kevin Conn, Sales Director, feels that the style (color scheme, graphics, fonts, etc.) of a Web site may affect its sales. He chooses three levels of design style (neon, old world and sophisticated) and randomly assigns six catalog Web sites to each design style. Analysis of Kevin's data yielded the following ANOVA table. Source of Variation
SS
df
MS
F Between Groups
68102.33
2
34051.17 Within Groups
29177.67
15
1945.178 Total
97280
17 Using a= 0.05, the critical F value is _____________.
a) 3.57
b) 19.43
c) 3.68
d) 19.45
e) 2.85
Q:
Pate's Pharmacy, Inc. operates a regional chain of 120 pharmacies. Each pharmacy's floor plan includes a greeting card department which is relatively isolated. Sandra Royo, Marketing Manager, feels that the level of lighting in the greeting card department may affect sales in that department. She chooses three levels of lighting (soft, medium, and bright) and randomly assigns six pharmacies to each lighting level. Analysis of Sandra's data yielded the following ANOVA table. Source of Variation
SS
df
MS
F Treatment
3608.333
2
1804.167 Error
13591.67
15
906.1111 Total
17200
17 Using a= 0.05, the appropriate decision is _____________.
a) do not reject the null hypothesism1 m2 m3
b) do not reject the null hypothesism1 = m2 =m3
c) reject the null hypothesism1 m2 m3
d) reject the null hypothesism1 m2 m3
e) inclusive
Q:
Medical Wonders is a specialized interior design company focused on healing artwork. The CEO, Kathleen Kelledy claims that artwork has healing effects for patients staying in a hospital, as measured by reduced length of stay. Her current client is a children's cancer hospital. Kathleen is interested in determining the effect of three different pieces of healing artwork on children. She chooses three paintings (a horse photo, a bright abstract, and a muted beach scene) and randomly assigns six hospital rooms to each painting. Analysis of Kathleen's data yielded the following ANOVA table. Source of Variation
SS
df
MS
F Treatment
33476.19
2
16738.1
9.457912 Error
26546.18
15
1769.745 Total
60022.37
17 Using a= 0.05, the critical F value is _____________.
a) 13.68
b) 19.43
c) 3.59
d) 19.45
e) 3.68
Q:
Medical Wonders is a specialized interior design company focused on healing artwork. The CEO, Kathleen Kelledy claims that artwork has healing effects for patients staying in a hospital, as measured by reduced length of stay. Her current client is a children's cancer hospital. Kathleen is interested in determining the effect of three different pieces of healing artwork on children. She chooses three paintings (a horse photo, a bright abstract, and a muted beach scene) and randomly assigns six hospital rooms to each painting. In Kathleen's experimental design "reduced length of stay" is _______.
a) the dependent variable
b) a concomitant variable
c) a treatment variable
d) a blocking variable
e) a constant
Q:
A human resources analyst is developing a regression model to predict electricity production plant manager compensation as a function of production capacity of the plant, number of employees at the plant, and plant technology (coal, oil, and nuclear). The "plant technology" variable in this model is ______.
a) a response variable
b) a dependent variable
c) a quantitative variable
d) an independent variable
e) a constant
Q:
A cost accountant is developing a regression model to predict the total cost of producing a batch of printed circuit boards as a linear function of batch size (the number of boards produced in one lot or batch), production plant (Kingsland, and Yorktown), and production shift (day, and evening). In this model, "shift" is ______.
a) a response variable
b) an independent variable
c) a quantitative variable
d) a dependent variable
e) a constant
Q:
The mean square error (MSerr) is calculated by dividing the sum of squares error (SSerr) by the number of error degrees of freedom (dferr).
Q:
Annie Mikhail, market analyst for a national company specializing in historic city tours, is analyzing the relationship between the sales revenue from historic city tours and the size of the city. She gathers data from six cities in which the tours are offered. Annie's dependent variable is annual sales revenues and her independent variable is the city population. Regression analysis of the data yielded the following tables. Coefficients
Standard Error
t Statistic
p-value Intercept
-0.14156
0.292143
-0.48455
0.653331 x
0.105195
0.013231
7.950352
0.001356 Source
df
SS
MS
F Se = 0.237 Regression
1
3.550325
3.550325
63.20809 r2 = 0.940483 Residual
4
0.224675
0.056169 Total
5
3.775 For a city with a population of 500,000, Annie's model predicts annual sales of ________________.
a) $70,780
b) $5,259
c) $170,780
d) $52,597
e) $152,597
Q:
Annie Mikhail, market analyst for a national company specializing in historic city tours, is analyzing the relationship between the sales revenue from historic city tours and the size of the city. She gathers data from six cities in which the tours are offered. Annie's dependent variable is annual sales revenues and her independent variable is the city population. Regression analysis of the data yielded the following tables. Coefficients
Standard Error
t Statistic
p-value Intercept
-0.14156
0.292143
-0.48455
0.653331 x
0.105195
0.013231
7.950352
0.001356 Source
df
SS
MS
F Se = 0.237 Regression
1
3.550325
3.550325
63.20809 r2 = 0.940483 Residual
4
0.224675
0.056169 Total
5
3.775 Annie's sample size is __________.
a) 2
b) 4
c) 6
d) 8
e) 10
Q:
Annie Mikhail, market analyst for a national company specializing in historic city tours, is analyzing the relationship between the sales revenue from historic city tours and the size of the city. She gathers data from six cities in which the tours are offered. Annie's dependent variable is annual sales revenues and her independent variable is the city population. Regression analysis of the data yielded the following tables. Coefficients
Standard Error
t Statistic
p-value Intercept
-0.14156
0.292143
-0.48455
0.653331 x
0.105195
0.013231
7.950352
0.001356 Source
df
SS
MS
F Se = 0.237 Regression
1
3.550325
3.550325
63.20809 r2 = 0.940483 Residual
4
0.224675
0.056169 Total
5
3.775 Annie's regression model can be written as: __________.
a) y = 7.950352 - 0.48455x
b) y = -0.48455 + 7.950352x
c) y = -0.14156 + 0.105195x
d) y = 0.105195 - 0.14156x
e) y = 0.105195 + 0.14156x
Q:
A manager wants to predict the cost (y) of travel for salespeople based on the number of days (x) spent on each sales trip. The following model has been developed: y = $400 + 120x. If a trip took 4 days, the predicted cost of the trip is _____________.
a) 480
b) 880
c) 524
d) 2080
e) 1080
Q:
In the regression equation, y=2.164+1.3657x n=6, the mean of x is 8.667, Sxx=89.333 and Se=3.44. A 95% prediction interval for y when x=8 is _________
a) (9.13, 17.05)
b) (2.75, 23.43)
c) (10.31, 15.86)
d) (3.56, 22.62)
e) (12.09, 14.09)
Q:
A researcher has developed a regression model from fourteen pairs of data points. He wants to test if the slope is significantly different from zero. He uses a two"‘ tailed test and a = 0.01. The critical table t value is _______.
a) 2.650
b) 3.012
c) 3.055
d) 2.718
e) 2.168
Q:
In a regression analysis if SST = 200 and SSR = 200, r 2 = _________.
a) 0.25
b) 0.75
c) 0.00
d) 1.00
e) -1.00
Q:
The proportion of variability of the dependent variable accounted for or explained by the independent variable is called the _______.
a) sum of squares error
b) coefficient of correlation
c) coefficient of determination
d) covariance
e) regression sum of squares
Q:
The numerical value of the coefficient of determination must be _______.
a) between -1 and +1
b) between -1 and 0
c) between 0 and 1
d) equal to SSE/(n-2)
e) between -100 and +100
Q:
A standard deviation of the error of the regression model is called the _______.
a) coefficient of determination
b) sum of squares of error
c) standard error of the estimate
d) R-squared
e) coefficient of correlation
Q:
The following residuals plot indicates _______________. a) a nonlinear relation
b) a nonconstant error variance
c) the simple regression assumptions are met
d) the sample is biased
e) the sample is random