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ECON 2330 Assignment#3 - Group (Check Moodle for your Group)
Winter 2019
Note: Once you completed these questions using the built-in
process under Data Analysis in Excel or Minitab to support your
results, you need to save the outputs of Excel or Minitab as a
picture and add it to your solutions in MS Word for each part of
these Problems, save all solutions as one PDF file and upload it in
Moodle. Otherwise, only partial mark will be given.
Problem#1 Parts (a). (c), and (d) of this Problem must be done
in Minitab, only solutions by Minitab will be given full mark.
To help consumers in purchasing a laptop computer, Consumer
Reports calculates an overall test score for each computer tested
based upon rating factors such as ergonomics, portability,
performance, display, and battery life. Higher overall scores
indicate better test results. The following data show the average
retail price and the overall score for ten 13-inch models (Consumer
Reports website, October 25, 2012).
Brand & Model Price ($) Overall Score
Samsung Ultrabook NP900X3C-A01US 1250 83 Apple MacBook Air
MC965LL/A 1300 83 Apple MacBook Air MD231LL/A 1200 82 HP ENVY
13-2050nr Spectre XT 950 79 Sony VAIO SVS13112FXB 800 77 Acer
Aspire S5-391-9880 Ultrabook 1200 74 Apple MacBook Pro MD101LL/A
1200 74 Apple MacBook Pro MD313LL/A 1000 73 Dell Inspiron
I13Z-6591SLV 700 67 Samsung NP535U3C-A01US 600 63
a) Develop a scatter diagram with price as the independent
variable.b) What does the scatter diagram developed in part (a)
indicate about the relationship
between the two variables?c) Use the Least Squares method to
develop the estimated regression equation.d) Provide an
interpretation of the slope of the estimated regression equation.e)
Another laptop that Consumer Reports tested is the Acer Aspire
S3-951-6646 Ultrabook;
the price for this laptop was $700. Predict the overall score
for this laptop using theestimated regression equation developed in
part (c).
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Problem#2 All parts of this Problem must be done in Excel, only
solutions by Excel will be given full mark.
The Dow Jones Industrial Average (DJIA) and the Standard &
Poor’s 500 (S&P 500) indexes are used as measures of overall
movement in the stock market. The DJIA is based on the price
movements of 30 large companies; the S&P 500 is an index
composed of 500 stocks. Some say the S&P 500 is a better
measure of stock market performance because it is broader based.
The closing price for the DJIA and the S&P 500 for 15 weeks,
beginning with January 6, 2012, follow (Barron’s website, April 17,
2012).
Date DJIA S&P January 6 12360 1278 January 13 12422 1289
January 20 12720 1315 January 27 12660 1316 February 3 12862 1345
February 10 12801 1343 February 17 12950 1362 February 24 12983
1366 March 2 12978 1370 March 9 12922 1371 March 16 13233 1404
March 23 13081 1397 March 30 13212 1408 April 5 13060 1398 April 13
12850 1370
a) Develop a scatter diagram with DJIA as the independent
variable. b) Develop the estimated regression equation. c) Test for
a significant relationship. Use α=0.05. d) Did the estimated
regression equation provide a good fit? Explain. e) Suppose that
the closing price for the DJIA is 13,500. Predict the closing price
for the
S&P 500. f) Should we be concerned that the DJIA value of
13,500 used to predict the S&P 500 value
in part(e) is beyond the range of the data used to develop the
estimated regression equation?
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Problem #3 All parts of this Problem must be done in Minitab,
only solutions by Minitab will be given full mark.
PC Magazine provided ratings for several characteristics of
computer monitors, including an overall rating (PC Magazine
website, April, 2015). The following data show the rating for
contrast ratio, resolution, and the overall rating for ten monitors
tested using a 0–100 point scale. The highest rated monitor was the
BenQ BL3201PH, with an overall rating of 87.
Model Contrast Ratio
Resolution Overall Rating
BenQ BL3201PH 78 89 87 AOC U2868PQU 98 87 86 NEC MultiSync
PA322UHD 84 82 85 Acer XB280HK 78 77 82 Asus ROG Swift PG278Q 65 82
82 AOC E1759Fwu 57 78 82 Dell UltraSharp UZ2715H 56 83 81 NEC
MultiSync EA244UHD 77 75 79 HP DreamColor Z27x 47 81 77 Dell
UltraSharp UZ2315H 55 70 76
a) Develop the estimated regression equation that can be used to
predict the Overall Rating using the Contrast Ratio Rating.
b) Develop the estimated regression equation that can be used to
predict the Overall Rating using both the Contrast Ratio Rating and
the Resolution Rating.
c) Predict the overall Overall Rating for a computer monitor
computer that has a Contrast Ratio Rating of 85 and a Resolution
Rating of 74.
Problem #4 All parts of this Problem must be done in Minitab
and/or Excel.
The Consumer Reports Restaurant Customer Satisfaction Survey is
based upon 148,599 visits to full-service restaurant chains
(Consumer Reports website, February 11, 2009). Assume the following
data are representative of the results reported. The variable type
indicates whether the restaurant is an Italian restaurant or a
seafood/steakhouse. Price indicates the average amount paid per
person for dinner and drinks, minus the tip. Score reflects diners’
overall satisfaction, with higher values indicating greater overall
satisfaction. A score of 80 can be interpreted as very
satisfied.
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Restaurant Type Price ($) Score Bertucci's Italian 16 77 Black
Angus Steakhouse Seafood/Steakhouse 24 79 Bonefish Grill
Seafood/Steakhouse 26 85 Bravo! Cucina Italiana Italian 18 84 Buca
di Beppo Italian 17 81 Bugaboo Creek Steak House Seafood/Steakhouse
18 77 Carrabba's Italian Grill Italian 23 86 Charlie Brown's
Steakhouse Seafood/Steakhouse 17 75 Il Fornaio Italian 28 83 Joe's
Crab Shack Seafood/Steakhouse 15 71 Johnny Carino's Italian Italian
17 81 Lone Star Steakhouse & Saloon Seafood/Steakhouse 17 76
LongHorn Steakhouse Seafood/Steakhouse 19 81 Maggiano's Little
Italy Italian 22 83 McGrath's Fish House Seafood/Steakhouse 16 81
Olive Garden Italian 19 81 Outback Steakhouse Seafood/Steakhouse 20
80 Red Lobster Seafood/Steakhouse 18 78 Romano's Macaroni Grill
Italian 18 82 The Old Spaghetti Factory Italian 12 79 Uno Chicago
Grill Italian 16 76
a) Develop the estimated regression equation to show how overall
customer satisfaction isrelated to the independent variable average
meal price.
b) At the 0.05 level of significance, test whether the estimated
regression equationdeveloped in part (a) indicates a significant
relationship between overall customersatisfaction and average meal
price.
c) Develop a dummy variable that will account for the type of
restaurant (Italian orseafood/steakhouse).
d) Develop the estimated regression equation to show how overall
customer satisfaction isrelated to the average meal price and the
type of restaurant.
e) Is type of restaurant a significant factor in overall
customer satisfaction?f) Predict the Consumer Reports customer
satisfaction score for a seafood/steakhouse that
has an average meal price of $20. How much would the predicted
score have changed foran Italian restaurant?
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Problem#5 All parts of this Problem must be done in Minitab
and/or Excel.
Over the past few years the percentage of students who leave
Lakeland College at the end of the first year has increased. Last
year Lakeland started a voluntary one-week orientation program to
help first-year students adjust to campus life. If Lakeland is able
to show that the orientation program has a positive effect on
retention, they will consider making the program a requirement for
all first-year students. Lakeland’s administration also suspects
that students with lower GPAs have a higher probability of leaving
Lakeland at the end of the first year. In order to investigate the
relation of these variables to retention, Lakeland selected a
random sample of 100 students from last year’s entering class. The
data are contained in the data set named Lakeland. The dependent
variable was coded as y=1 if the student returned to Lakeland for
the sophomore year and y=0 if not. The two independent variables
are:
a) Write the logistic regression equation relating X1 and to X2
.b) What is the interpretation of E (y ) when X2=0?c) Use both
independent variables and Minitab to compute the estimated logit.d)
Conduct a test for overall significance using Use α=0.05.e) Use
α=0.05 to determine whether each of the independent variables is
significant.f) Use the estimated logit computed in part (c) to
estimate the probability that students with a 2.5
grade point average who did not attend the orientation program
will return to Lakeland for theirsophomore year. What is the
estimated probability for students with a 2.5 grade point average
whoattended the orientation program?
g) What is the estimated odds ratio for the orientation program?
Interpret it.h) Would you recommend making the orientation program
a required activity? Why or why not?
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All parts of this Problem must be done in Excel.
Problem#6: The Transactional Records Access Clearinghouse at
Syracuse University reported data showing the chance of an Internal
Revenue Service (IRS) audit. The data in file IRSAudit show the
average adjusted gross income reported (in $ thousands) and the
percent of the returns that were audited for 20 selected IRS
districts.
a. Use EXCEL to create a scatterplot with average adjusted gross
income reported on thehorizontal axis and percent of the returns
that were audited on the vertical axis. Includethe fitted simple
linear regression line on the plot and include the plot in your
answer.What does the scatterplot indicate about the relationship
between the average adjustedgross income reported and the percent
of the returns that were audited?
b. Use EXCEL to estimate a simple linear regression model using
least squares. Report theestimated regression equation that could
be used to predict the percent audited given theaverage adjusted
gross income reported.
c. Is there a significant linear relationship between the two
variables based on asignificance level 𝛼𝛼 = 0.05?
d. Use the estimated regression equation to predict the percent
audited for a district with anaverage adjusted gross income of
$35,000.
e. Use EXCEL to compute a 95% confidence interval for the
average percent audited ofdistricts with an average adjusted gross
income of $35,000. Interpret the interval in thecontext of the
application.
f. Use EXCEL to compute a 95% prediction interval for the
percent audited of an individualdistrict with an average adjusted
gross income of $35,000. Interpret the interval in thecontext of
the application.
g. Use the regression output in EXCEL to calculate the
coefficient of determination, 𝑟𝑟 2from the sum of squares due to
regression (SSR) and the total sum of squares (SST).Interpret your
calculated value of 𝑟𝑟 2 in the context of the application.
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h. The following plots were created from the estimated simple
linear regression model fitto this dataset.
We can characterize the left-hand plot as a random cloud of
points in a rough horizontal band and the right-hand plot as points
that lie reasonably close to the 45° line. Briefly describe what
this tells us about the simple linear regression model assumptions
in this case.
i. The largest absolute standardized residual for this simple
linear regression analysis is1.703, while the highest leverage is
0.237. Briefly describe what this tells us aboutpotentially
influential observations in this analysis. An auditor notes that
the coefficientof determination is relatively low for this analysis
and hence the least squares line doesnot provide a very good fit
and the model has little value. Do you agree with thisassessment?
Why or why not?
All parts of this Problem must be done in Excel. Problem#7: A
factorial experiment was designed to test for any significant
differences in the time needed to perform English to foreign
language translations with two computerized language translator
systems. Because the type of language translated was also
considered an important factor, translations were made with both
systems for three different languages: Spanish, French, and German.
The data for translation time in hours are contained in the file
Translations. Use a significance level 𝛼𝛼 = 0.05 to test for
differences due to language translator system, type of language,
and interaction.
a. Use EXCEL to compute the p-values for system, language, and
the interaction.
b. What are your hypothesis test decisions for each of system,
language, and theinteraction?
c. What are your conclusions in the context of the application?
Your conclusions shouldrelate back to the question.
Pred(Percent Audited) / Standardized residuals Q-Q plot (Std.
residual)
2 2
1.5 1.5
1 1
0.5 0.5
0 0 0.6 0.7 0.8 0.9 1 1.1 -2 -1 0 1 2
-0 .5 -0 .5
-1 -1
-1 .5 -1 .5
-2 Pred(Percent Audited) Std. residual
-2
Stan
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Qua
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.95)
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Parts 4, 5, 6 of this Problem must be done in Excel. Problem # 8
Suppose that a local chapter of sales professionals conducted a
survey of its membership to study the relationship, if any, between
the years of experience and salary for individuals employed in
inside and outside sales positions. On the survey, respondents were
asked to specify one of three levels of years of experience: low
(1–10 years), medium (11–20 years), and high (21 or more years). A
portion of the data obtained follow. The complete data set,
consisting of 120 observations, is contained in the file named
SalesSalary.
1. Use descriptive statistics to summarize the data.2. Develop a
95% confidence interval estimate of the mean annual salary
for all salespersons, regardless of years of experience and type
ofposition.
3. Develop a 95% confidence interval estimate of the mean salary
foroutside salespersons.
4. Use analysis of variance to test for any significant
differences due toposition. Use a 0.05 level of significance, and
for now, ignore theeffect of years of experience.
5. Use analysis of variance to test for any significant
differences due toyears of experience. Use a .05 level of
significance, and for now,ignore the effect of position.
6. At the 0.05 level of significance test for any significant
differencesdue to position, years of experience, and
interaction.
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