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Time Series and Categorical Variables

Course Details (Treatment of engineering data using the concepts of frequency distribution; measures of central tendency and dispersion. Probability; random variables; discrete and continuous distributions. Tests of hypotheses; estimation; goodness-of-fit test; linear regression and correlation. Applications using computers in engineering design problems, quality control, and manufacturing processes).

the title is (Time Series and Categorical Variables)

Home Exercises #6
Time Series and Categorical Variables

PROBLEM 1 [15 pts]
File DollarEuro-2012.xls contains a record of daily US dollar/euro exchange rate for the 3 months from Dec. 1, 2011 through Feb. 29, 2012 (n=65 days). For this data set:
a. [ 5pts] Describe the pattern
b. [10 pts] Use Excel’s Moving Average function and describe the effect of increasing m (e.g., m = 2, 4, 7, etc.). Include at least three graphs with your answers.

PROBLEM 2 [25 pts]
File DeckSealer.xls contains weekly sales of a deck sealer (a paint product sold in gallon-size containers) at a large do-it-yourself warehouse-style retailer. For this data set:
a. [10 pts] Plot the raw data and create a histogram
b. [10 pts] Calculate the forecast values for the exponential smoothing average with smoothing coefficient α = 0.10. Use two ways of initializing the process (see lecture notes):
• Method A: use the first data value (set F1 = y1)
• Method B: average the first 6 data values (set F1 = (y1+…+y6)/6
c. [5 pts] Compare (plot) and comment on the resulting differences

PROBLEM 3 [20 pts]
The table classifies movies released in a particular year by genre and MPAA rating

G PG PG-13 R Total
Action/Adventure 66.7 25.0 30.4 23.7 29.2
Comedy 33.3 60.0 35.7 10.5 31.7
Drama 0 15 14.3 44.7 23.3
Thriller/Horror 0 0 19.6 21.1 15.8
Total 100% 100% 100% 100% 100%

a. [5 pts] What percentage of these movies were comedies?
b. [5 pts] What percentage of the PG-rated movies were comedies?
c. [10 pts] Which of the following can you learn from this table? Give the answer if you can find it from the table.
(1) The percentage of PG-13 movies that were comedies.
(2) The percentage of dramas that were R-rated.
(3) The percentage of dramas that were G-rated.
(4) The percentage of 2005 movies that were PG-rated comedies.

PROBLEM 4 [25 pts]
A survey of cars parked in the student and staff lots at a large university classified the brands by country of origin, as shown in the table.

Origin Student Staff
American 107 105
European 33 12
Asian 55 47

a. What percent of all the cars surveyed were foreign?
b. What percent of the American cars were owned by the students?
c. What percent of the students owned American cars?
d. What is the marginal distribution of cars’ origin?
e. Do you think that the origin of the car is independent of the type of the driver? Explain.

PROBLEM 5 [25 pts]
A small grocery store would like to know if the number of items purchased by a customer is independent of the type of payment method the customer chooses to use. Having this information can help the store manager determine how to set up various checkout lanes. The manager collected a random sample of 368 customer transactions. The results are show in the following table:

# of items Cash Check Credit/Debit card
1-5 30 15 43
6-10 46 23 66
10-20 31 15 43
20+ 19 10 27

a. Of all the items purchased, what proportion was paid by cash? How does cash payment depend on the number of items purchased?
b. Of the large number of items purchased, what proportion was paid by a credit/debit card?
c. Create a segmented bar graph displaying the conditional distribution of number of purchases.
d. Create a segmented bar graph displaying the conditional distribution of items paid by each method.
e. Considering your answers to (a), (b) and the segmented bar graphs in (c) and (d), should the manager set up the cash-only checkout lane? Provide your reasoning.


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