If a regression model with k independent variables has a C statistic less than _______,
then the model is considered to be desirable.
A. k + 1
B. k
C. k – 1
D. 1/k
E. k – 2
The range of feasible values for the multiple coefficient of correlation is from
________.
A.
B. -1 to 0
C. -1 to 1
D. 0 to 1
E.
In multiple regression analysis, which one of the following is the appropriate notation
for error (residual)?
A. Option A
B. Option B
C. Option C
D. Option D
E. Option E
The _____ distribution is used for testing the significance of the slope term.
A. t
B. z
C. r
D. r2
For the same value of X (independent variable), the confidence interval for the average
value of Y (dependent variable) is __________________ the prediction interval for the
individual value of Y.
A. Larger than
B. Smaller than
C. The same as
D. Sometimes larger than, sometimes smaller than
Observing the output of a process at fixed time intervals is referred to as ___________
sampling.
A. Consecutive
B. Random
C. Fixed
D. Periodic
The χ2 statistic is used to test whether the assumption of normality is reasonable for a
given population distribution. The sample consists of 5000 observations and is divided
into 6 categories (intervals). The degrees of freedom for the chi-square statistic are:
A. 4999
B. 6
C. 5
D. 4
E. 3
If it is desired to include marital status in a multiple regression model by using the
categories single, married, separated, divorced, and widowed, what will be the effect on
the model?
A. One more independent variable will be included.
B. Two more independent variables will be included.
C. Three more independent variables will be included.
D. Four more independent variables will be included.
E. Five more independent variables will be included.
A study of car accidents and drivers who use cell phones collects the following sample
data.
Calculate the chi-square statistic for this test of independence.
The _____________ measures the strength of the linear relationship between the
dependent variable and the independent variable.
A. Correlation coefficient
B. Distance value
C. Y-Intercept
D. Residual
A manufacturing company produces part A732 for the aerospace industry. This
particular part can be manufactured using 3 different production processes. The
management wants to know if the quality of the units of part A732 is the same for all
three processes. The production supervisor obtained the following data: Process 1 had
29 defective units in 240 items, Process 2 produced 12 defective units in 180 items, and
Process 3 manufactured 9 defective units in 150 items.
Chi-Square Contingency Table Test for Independence
At a significance level of .05, the management wants to perform a hypothesis test to
determine if the quality of the items produced appears to be independent of the
production process used. Based on the results summarized in the MegaStat/Excel output
provided in the table above, we:
A. Reject H0 and conclude that the quality of the product is not the same for all
processes.
B. Reject H0 and conclude that the quality of the product is dependent on the
manufacturing process.
C. Do not reject H0, and conclude that the quality of the product does not significantly
differ among the three processes.
D. Do not reject H0, and conclude that the quality of the product is not the same for all
processes.
E. Reject H0 and conclude that the quality of the product is independent of the
manufacturing process used.
___________ causes of variation may be remedied by local supervision.
A. Common
B. Assignable
C. Usual
D. Expected
The χ2 goodness-of-fit test requires the nominative level of data.
If one of the assumptions of the regression model is violated, performing data
transformations on the ____________ can remedy the situation.
A. independent variable
B. slope
C. predictor variable
D. response variable
Different levels of a factor are called ____________.
A. Treatments
B. Variables
C. Responses
D. Observations
The following results were obtained as part of a simple regression analysis:
The null hypothesis of no linear relationship between the dependent variable and the
independent variable:
A. Is rejected.
B. Cannot be tested with the given information.
C. Is not rejected.
D. Is not an appropriate null hypothesis for this situation.
A manufacturing company produces part A732 for the aerospace industry. This
particular part can be manufactured using 3 different production processes. The
management wants to know if the quality of the units of part A732 is the same for all
three processes. The production supervisor obtained the following data: Process 1 had
29 defective units in 240 items, Process 2 produced 12 defective units in 180 items, and
Process 3 manufactured 9 defective units in 150 items. At a significance level of .05,
the management wants to perform a hypothesis test to determine whether the quality of
items produced appears to be independent of the production process used. What is the
rejection point condition?
A. Reject H0 if χ2 > .10257
B. Reject H0 if χ2 > 9.3484
C. Reject H0 if χ2 > 5.99147
D. Reject H0 if χ2 > 7.37776
E. Reject H0 if χ2 > 7.81473
R2 is defined as:
A. Total variation/explained variation.
B. Explained variation/total variation.
C. Unexplained variation/explained variation.
D. Unexplained variation/total variation.
The mean square error of a multiple regression model with k independent variables and
n observations is __________.
A. SSE/n
B. SSE/[n + (k + 1)]
C. SSE/[n – (k + 1)]
D. SSE/(k + 1)
In performing a chi-square goodness-of-fit test for a normal distribution, a researcher
wants to make sure that all of the expected cell frequencies are at least five. The sample
is divided into 7 intervals. The second through the sixth intervals all have expected cell
frequencies of at least five. The first and the last intervals have expected cell
frequencies of 1.5 each. After adjusting the number of intervals, the degrees of freedom
for the chi-square statistic is ____.
A. 2
B. 3
C. 5
D. 7
If the Durbin-Watson statistic is less than dL, then we conclude that:
A. There is significant positive autocorrelation.
B. There is significant negative autocorrelation.
C. There is significant autocorrelation, but we cannot identify whether it is positive or
negative.
D. The test results are inconclusive.
If there is significant autocorrelation present in a data set, the ________________
assumption is violated.
A. Normality
B. Independence of error terms
C. μ = 0
D. Constant variation
Stepwise regression uses a series of ___________ tests during each iteration in order to
determine which independent variables should be brought into the regression model.
A. C
B. Chi-square
C. t or F
D. VIF
Unusual sources of process variation that can be attributed to specific reasons are called
____________ causes of variation.
A. common
B. assignable
C. usual
D. expected
The assumption of independent error terms in regression analysis is often violated when
using time-series data.
In general, a Tukey simultaneous 100(1 – α) percent confidence interval is _________
than the corresponding individual 100(1 – α) percent confidence interval.
A. Wider
B. Narrower
C. No different
D. Two times more
In simple regression analysis, the quantity is called the __________ sum of
squares.
A. Total
B. Explained
C. Unexplained
D. Error
A sum of squares that measures the total amount of variability in the observed values of
the response variable is referred to as the:
A. Treatment sum of squares.
B. Error sum of squares.
C. Sum of squares within-treatment.
D. Total sum of squares.
E. Interaction sum of squares.
___________ simultaneous confidence intervals test all of the pairwise differences
between means, respectively, while controlling the overall Type I error.
A. Randomized
B. Tukey
C. Covariate
D. Interacting
A study of car accidents and drivers who use cell phones collects the following sample
data.
At a significance level of 0.05, determine the appropriate degrees of freedom and the
rejection point condition for the test.
The distance between natural tolerance limits and customer specifications is called
____________.
A. process leeway
B. sigma level
C. control limits
D. a zone
When the assumption of __________ residuals (error terms) is violated, the
Durbin-Watson statistic is used to test to determine if there is significant
_____________ among the residuals.
A. Normality, probability
B. Independent, probability
C. Independent, autocorrelation
D. Normality, autocorrelation
In a simple linear regression model, the intercept term is the mean value of y when x
equals _____.
A. 1
B. 0
C. -1
D. y
Consider the following partial analysis of variance table from a randomized block
design with 6 blocks and 4 treatments.
Calculate the degrees of freedom for blocks.
AAA Co. operates distribution centers in the Midwest. Three of their centers were
recently audited to determine if they are in compliance with company standard billing
procedures. According to the auditing firm, a billing had an equal probability of being
from each of the three centers. A random sample of the audited billings had the
following distribution:
What are the degrees of freedom for the χ2 test?
Consider a two-way analysis of variance experiment with treatment factors A and B,
with factor A having four levels and factor B having three levels. The results are
summarized below.
Calculate the degrees of freedom for the interaction between Factors A and B.
An experiment was performed on a certain metal to determine if the strength is a
function of heating time. Results based on 10 metal sheets are given below. Use the
simple linear regression model.
Calculate the coefficient of determination.
A county has four major hospitals: (1) Regional Memorial, (2) General, (3) Charity, and
(4) City. A multiple regression model is used to compare the time spent in these
hospitals after a heart bypass surgery. The response variable is the amount of time spent
in the hospital (in days). The quantitative independent variables include the age of the
patient, cholesterol level of the patient, and blood pressure of the patient. Define the
dummy variables so that all other hospitals are compared to City Hospital (base).
Consider the following partial computer output for a multiple regression model.
How many observations were taken?
Consider the randomized block design with 4 blocks and 3 treatments given above.
What are the degrees of freedom for error?
The HR manager of a major office supply chain is interested in determining whether
employee educational level affects knowledge of their job. An exam was given to 120
employees. The results are below:
For each row total, calculate the corresponding percentage.
The manufacturer of a light fixture believes that the dollars spent on advertising, the
price of the fixture and the number of retail stores selling the fixture in a particular
month influence the light fixture sales. The manufacturer randomly selects 10 months
and collects the following data:
The sales are in thousands of units per month, the advertising is given in hundreds of
dollars per month, and the price is the unit retail price for the particular month. Using
MINITAB, the following computer output is obtained.
Based on 30 time-ordered observations from a simple regression, we have determined
the Durbin-Watson statistic, d = 2.71. At α = .05, test to determine if there is any
evidence of negative autocorrelation. State your conclusions.
Below is a partial multiple regression computer output.
Test the usefulness of variable x5 in the model at α = .05. Calculate the t statistic and
state your conclusions.
A local tire dealer wants to predict the number of tires sold each month. He believes
that the number of tires sold is a linear function of the amount of money invested in
advertising. He randomly selects 6 months of data consisting of tire sales (in thousands
of tires) and advertising expenditures (in thousands of dollars). Based on the data set
with 6 observations, the simple linear regression model yielded the following results.
Calculate the coefficient of determination.
On the most recent tax cut proposal, a random sample of Democrats and Republicans in
the Congress cast their votes as follows:
At a significance level of .01, determine the appropriate degrees of freedom and the
rejection point condition for this test.
Consider the following calculations for a one-way analysis of variance from a
completely randomized design with 20 total observations. The response variable is sales
in millions of dollars and four treatment levels represent the four regions that the
company serves.
Perform a pairwise comparison between treatment mean 1 and treatment mean 4 by
computing a Tukey 95 percent simultaneous confidence interval.
The following frequency table summarizes the ages of 60 shoppers at the local grocery
store.
The estimated mean is 36.25 and estimated standard deviation is 13.57. Calculate the
probability for each interval, assuming a normal distribution.
Consider the following partial analysis of variance table from a randomized block
design with 6 blocks and 4 treatments.
What is the mean square error?
The AAA Co. is interested in the level of satisfaction of their employees in the benefit
package that they offer compared to their major competitors. A consultant hired to
conduct the satisfaction survey told AAA Co. that the distribution of level of
satisfaction at other companies is displayed below:
A survey was conducted of 125 AAA employees with the following results:
Using the critical value for α = .05, test the null hypothesis that the distribution of AAA
employees at each satisfaction level is similar to the distribution of the employees of
their major competitors.
The following frequency table summarizes the ages of 60 shoppers at the local grocery
store.
The estimated mean is 36.25, and the estimated standard deviation is 13.57. It is desired
to test whether these measurements came from a normal population. What is the df for
this chi-square test of normality?