## (solution) business statistics assessment, the topic is time series and

business statistics assessment, the topic is time series and index numbers.

Assessment task for Time series/ Index Numbers sem 1 2016

handing in

Firstly fill in section A Print off and complete before Name : Section A (2 marks)

Your student number is S 3 4 8 3 0 6 1 You will make some numbers using your student number

The first number, to be used in question 1, is the first two digits of your student number Now referred as A The second number will also be used in Question 1. It is made from the last two digits in your student

number

Now referred as B The Third number will be used Question 1, and is made using the third and fourth digits of your student

number

Now referred as C The Fourth number will also be used Question 1, and is made using the Fourth and fifth digits of your

student number

Now referred as D The Fourth number will be used Question 1, and is made using the first and sixth digits of your student

number

Now referred as E Eight numbers to be used in Question 2 will be made from the digits 1 First

Digit 1 Second

Digit 1 Sixth

Digit 1 Seventh

Digit 1 Third

Digit And also 1 Fourth

Digit 1 Fifth

Digit Your age 22 List the 8numbers you will be using in the box below, And this will be referred to as data set F Question 1 (11 marks) Document: qattachments_5893efc52e493164100db49fd177530352659dfa.doc

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Page 1 of 4 The price of Two hats, the ?regency?, and also the ?Dapper? for the years 2010, 2012 and 2015

are listed below. This is the cost for a single hat in \$.

Hat

Regency

Dapper 2010

\$25.00

\$ C 2012

\$ B

\$23.00 2015

\$26.00

\$E a) Using 2010 as the base year calculate the Simple Price index for each of the hats in 2015 ( 1 + 1 marks)

b) Use the above information to calculate the Simple aggregate index for 2012 using 2010 as the base year

Interpret your answer ( 3+ 1 marks) The actual numbers (quantity) of hats sold for each of the years were:

room

Regency

Dapper 2010 2012 2015 A

C B

D C

A c) Calculate the Laspeyres index for 2015 using 2010 as the base year. Interpret your answer.

( 4 + 1 marks) Question 2 (20 marks)

The following table represents the number of enrolments in a first year business statistics course over an

eight year period: Place your data set F Starting from the first number in row 1 down to the last in row 8

Document: qattachments_5893efc52e493164100db49fd177530352659dfa.doc

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Page 2 of 4 Year Enrolments 1

2

3

4

5

6

7

8 MA (3 year) Regression line

predictions Errors for the

regression line

predictions Error ^2 ----------- I. Calculate the 3 year Moving Average forecast and complete the MA (3 year) column above. II. Using the regression line Enrolments = 0.85(Year) + 11 + ?1 + ?2

Where ?1 = - 5 for years 1, 3, 5, 7

And ?2 = + 4 for years 2, 4, 6, 8 Predict the enrolment for each of the years and complete the fourth column? Regression line

predictions?

III. Calculate the errors for regression line prediction, and complete the 5th column IV. Calculate the Mean Absolute Deviation (MAD) for Regression V. Calculate the MSE (Mean Square of Errors ) for Regression VI

Graph your first two table columns (Year and enrolments) as a time series below and describe

the plot ( Be mindful of trend, and cyclic variation ( if any) ) ( 5 + 4 + 3 + 2 + 2 + 4) Question 3 (7 marks) a. If you had the following monthly data

Month

January Profit (\$)

2400

Document: qattachments_5893efc52e493164100db49fd177530352659dfa.doc RMIT University Save Date: 16/10/2016

Page 3 of 4 February

3200

March

2050

April

The forecast for April using a 3 month moving average would be

A. 3200

B. 2060

C. 2550

D. None of the above

b If you had the following monthly data

Month

Actual

January

2200

February

3000

March

2500

April

3500

The Mean Absolute Deviation (MAD) would be _______.

A. 600

B. 150

C. 3500

D. 100

c. If you had the following weekly data

Week

1

2

3

4 Predicted

2100

3200

2500

3400 Actual

90

102

96

99 Predicted

92

101

97

97 The Mean Square of Errors (MSE) would be _______.

A. 18

B. 5

C. 36

D. 2.5

( 1 mark each)

d. Give an everyday example of the following components in time series

Irregular variation

Seasonal variation

Cyclic variation

Trend ( 1 mark each) Document: qattachments_5893efc52e493164100db49fd177530352659dfa.doc

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