STAT 351 Final Exam - Summer 2 XXXXXXXXXX100 Points
This is a take home exam and it must be done individually. You are not allowed to discuss this
exam with others.
• Due date: Friday, July 31, 2020 at 11.59 p.m. CDT.
You are given 36 hours to write your answers and submit your exam through one of the three
methods given below.
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esponding question
number and co
esponding parts of the questions (Ex: an image name could be Q3. a, b, c).
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2. If your answers are handwritten, they must be LEGIBLE/READBLE.
3. Write your answers in order as given in the exam.
• Warning:
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grades. So, make use of the time to carefully prepare your exam.
• Direction:
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esponding
parts of the questions. Ex: Q3. c
2. Write your answers in order as given in the exam.
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Q1. The following Regression function has been developed to check the relationship between the
dependent variable y and the independent variable ?1.
Consider the following Minitab output and answer the questions.
Regression Equation
�̂� = ?. ?? + ?. ?? ??
a) (4pt). Please fill out the Coefficients table appropriately.
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant (i XXXXXXXXXX
?? (ii XXXXXXXXXX.00
) (4pt). Please fill out the ANOVA table appropriately.
Analysis of Variance
Source DF SS MS F
Regression (iii XXXXXXXXXX
17.37 E
or (iv) (v) 0.12
Total 9 3.10
c) Suppose that variables ?2 ??? ?3 are added to the above model and the following regression
analysis is obtained.
Regression Analysis: Y versus X1, X2, X3
The regression equation is
�̂� = XXXXXXXXXX ? XXXXXXXXXX ? XXXXXXXXXX ?3
Term Coef SE Coef T
Constant XXXXXXXXXX
X1 (vi XXXXXXXXXX
X2 (Vii XXXXXXXXXX
X XXXXXXXXXX
(4pt). Please fill out the above Coefficients table appropriately.
d) (8pt). Please fill out the ANOVA table appropriately based on the information from part (c).
Analysis of Variance
Source DF SS MS F
Regression (viii XXXXXXXXXXxii) (xiii)
E
or (ix) (xi) 0.06
Total (x) 3.11
Q2. The following time series shows the number of units of a product sold over the past six months.
Month
Units Sold
(Thousands)
1 9
2 3
3 6
4 6
5 12
6 9
Consider the following 3-month moving average for the above time series and forecast the sales
volume for month 7.
Month
Units Sold
(Thousands)
3-month moving
average
Forecast (F) e
or
Squared
E
or
1 9 * * * *
2 3 * * * *
3 6 6 * * *
4 6 5 (i)? 0 0
XXXXXXXXXX
XXXXXXXXXXiii)? (iv)?
7 (ii)?
a) (4pt) Compute the number (i): Show your work for full credit
) (4pt) Compute the number (ii): Show your work for full credit
c) (3pt) Compute the number (iii): Show your work for full credit
d) (3pt) Compute the number (iv): Show your work for full credit
e) (6pt) What is the mean square e
or (MSE)? (Recall: E
or =Actual value - Forecast value).
Show your work for full credit
Q3.
Based on the time series values from problem number 2, consider the following table of
exponential smoothing values using ? = ?. ? for the time series.
Month
Units Sold
(Thousands)
Forecast (F) e
or Squared e
or
1 9 * * *
2 3 (i)? (ii)? 36
XXXXXXXXXX.44
XXXXXXXXXX.7056
XXXXXXXXXX29.2897
XXXXXXXXXX6216
7 (iii)?
a) (3pt) Compute the number (i): Show your work for full credit
) (3pt) Compute the number (ii): Show your work for full credit
c) (5pt) Compute the number (iii): Show your work for full credit
d) (6pt) What is the mean square e
or (MSE)? Show your work for full credit
e) (6pt) Compare the MSE for part (Q3.d) using exponential smoothing values and (Q2.e)
using the 3-month moving average. Which method is better and why?
Q4.
The following data show the quarterly sales of Amazing Graphics, Inc. for the years 1 through 3.
Year Quarter Time Period (t) Sales (1000s)
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
From the above data, it could be concluded that both quarterly seasonal effects and linear trend in
the sales pattern are present. A time series model was considered for this question and the
estimated regression equation from Minitab is found as follows:
?�̂�(?????) = ?. ?? − ?. ?? ???????_? + ?. ?? ???????_? + ?. ?? ???????_? + ?. ? ?,
where, ?�̂� = Estimated or forecasted sales in period t,
? = ???? ?????? (where t = 1 for Quarter 1 of year 1 and t = 12 for Quarter 4 of year 3),
Quarter_2 = {
1 ?? ???? ?????? ? ??????????? ?? ?ℎ? ?????? ??????? ?? ?ℎ? ????
0 ??ℎ??????,
Quarter_3 = {
1 ?? ???? ?????? ? ??????????? ?? ?ℎ? ?ℎ??? ??????? ?? ?ℎ? ????
0 ??ℎ??????,
Quarter_4 = {
1 ?? ???? ?????? ? ??????????? ?? ?ℎ? ?????ℎ ??????? ?? ?ℎ? ????
0 ??ℎ??????.
a) (4pt) Please find the estimated sales for the first quarter for the next year (year 4).
Please show your work for full credit.
) (4pt) Please find the estimated sales for the fourth quarter for the next year (year 4).
Please show your work for full credit
Q5. The Dream Star Foundation used a survey to determine if the selection of a TV station is
independent of the level of education (DreamWeek , January 25, XXXXXXXXXXFrom a poll of 800
television viewers, the following data have been obtained as to their levels of education and their
preference of television stations. We are interested in determining if the selection of a TV station
is independent of the level of education.
Television stations
Educational Level
High School Bachelor Graduate TOTAL
Public Broadcasting XXXXXXXXXX
Commercial Stations XXXXXXXXXX
TOTAL XXXXXXXXXX
a) (2pt) State the null and alternative hypotheses.
) (6pt) Calculate the expected frequency. Show your work for full credit.
c) (4pt) Compute chi-square statistic (?2). Show your work for full credit.
d) (3pt) Find the degrees of freedom and the table value from the chi-square. Show your
work for full credit.
e) (3pt) Draw your conclusion. State your conclusion in