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MIS171 BUSINESS ANALYTICS

DEAKIN UNIVERSITY FACULTY OF BUSINESS AND LAW DEPARTMENT OF INFORMATION SYSTEMS AND BUSINESS ANALYTICS SAMPLE EXAMINATION PAPER (1) MIS171 BUSINESS ANALYTICS SAMPLE SOLUTIONS

MIS171 Business Analytics

Sample Exam 1

QUESTION 1 (a) The following summary statistics relate to information collected from the sampled 150 Bendigo Regional Businesses which included Managers Annual Salary (in $ ‘000). Ten of these salaries are summaries and presented in the table below.

Manager Annual Salary ($'000) Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Q1 Q3 IQR

100.6 19.0 90.6 #N/A 60.2 3624.3 6.1 2.3 209.9 48.2 258.1 1006.1 10.0 61.9 112.1 50.2

(i) What is the shape of the distribution of the data for the variable “ManagerAnnualSalary”?

The skewness coefficient is +2.3 The data set is highly positively/right skewed (ii)

Explain how you arrived at your answer in part (i).

The mean (100.6) is larger than the median (90.6) Distribution has a positive skewness coefficient of 2.3

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MIS171 Business Analytics

Sample Exam 1

(b) Based on the summary measures and your answers for parts (a) and (b) above, write a brief DOT POINT summary in plain language about the variable ‘ManagerAnnualSalary’, summarising its most important features.

Using Tukey’s approach, there is an unusually large value on the right of the distribution: =112.1+(1.5*50.2) > 187.4 (there is at least 1 unusually large value of 258.1) From these 10 observations •

the average salary is $90,600.

•

The minimum salary is $48,200 and the maximum salary is $258,100.

•

Revealing a range in salaries of 209,900

•

The middle 50% of salaries cover a range of $50,200. From $61,900 to $112,100. This represents considerable variation.

•

25% of salaries are less than $61,900.

•

25% of salaries are greater than $112,100.

•

Compared to all other managers in this sample, there is one manager who has an unusually large salary of $258,100.

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MIS171 Business Analytics

Sample Exam 1

QUESTION 2 It is thought that metropolitan managers make more money than regional managers, however, this gap is said to be closing. Councillors are interested in checking whether there is a difference in the salary of local regional business managers compared to the salary of metropolitan business managers. Summary statistics from a sample of 100 regional and metropolitan business managers are presented below. Note: Metropolitan managers work in densely populated areas whereas regional managers work in sparsely populated areas.

Metropolitan Manager Annual Salary ($'000) Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Count Q1 Q3 IQR (a)

Regional Manager Annual Salary ($'000) 93.10588 3.618117 97.5 #N/A 14.91788 222.5431 -0.08774 -0.50013 57 62.7 119.7 83 86.9 103.1 16.2

Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Count Q1 Q3 IQR

78.56024 2.494088 78.6 #N/A 22.72222 516.2995 1.033902 0.61495 126.1 36.4 162.5 17 62.95 92.75 29.8

Which of the above sample statistics would be the most useful to use to compare local regional business managers salary to the salary of metropolitan business managers? Explain your choice.

As the data is not badly skewed (skew coefficients not larger than 1 or smaller than -1), the best measure of central tendency to compare would be the mean. Because we are comparing the mean, the best measure of variability to compare would be the standard deviation. Comparing the range allows consideration of comparative spread and incorporating the Min and Max comparison, allows an understanding of where that range actually is. Other comparisons are informative, but the above comparisons are the most useful. OR As the metropolitan managers’ annual average mean salary is slightly less than the median salary, the data might be slightly skewed to the left. Therefore a comparisons of the medians would be useful. Page 4 of 13

MIS171 Business Analytics

Sample Exam 1

Comparative variability can be considered by comparing the interquartile ranges, as well as comparing the proportion of observations that exist in the distribution above and below the various quartiles (75% above and 25% below Q1, and 75% below and 25% above Q3 for example). Comparing the range allows consideration of comparative spread and incorporating the Min and Max comparison, allows an understanding of where that range actually is. Other comparisons are informative, but the above comparisons are the most useful. (b)

Describe the relationship (if any) in plain language between managers’ annual salaries and location using key figures from the above comparative summary measures.

MEAN COMPARISON APPROACH (comparing means and StDevs)

1. Compared to regional managers, metropolitan managers are, on average, earning more in annual salary. ($93,100 compared to $78,600). A difference of $14,500. 2. There appears to be much more variability in regional salaries (average spread of $22.7K around its typical value) compared to metropolitan salaries (average spread of $14.9K around its typical value). 3. 50% of metropolitan salaries ($97,500 or more) are greater than three quarters of regional salaries ($92,750 or less). However, the manager with the largest salary ($162,500) is a regional manager. ..or other suitable comparisons..

OR MEDIAN COMPARISON APPROACH (comparing medians and IQR’S)

1. Compared to regional managers, metropolitan managers are, on average, earning more in annual salary. ($97,500 compared to $78,600). A difference of $18,900. 2. The middle 50% of salaries for regional managers falls between $62,950 and $92,750 (range of $29,800), yet for metropolitan managers the middle 50% of salaries falls between $86,900 and $103,100 (range of $16,200). Whilst metropolitan mangers’ salaries are generally higher, there is clearly more variability in the salaries of regional managers. 3. 50% of metropolitan salaries ($97,500 or more) are greater than three quarters of regional salaries ($92,750 or less). However, the manager with the largest salary ($162,500) is a regional manager ..or other suitable comparisons..

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MIS171 Business Analytics

Sample Exam 1

QUESTION 3 The Bendigo Chamber of Commerce wants to know if there is any evidence of a relationship between how a business perceives their prospect for future investment and whether or not that business has a growth strategy. Prospect for future investment is measured as: 1 Low, 2 Neither Low nor High, and 3 High. Growth strategy is measured as: 1 Yes and 2 No. (a)

Determine the scale of measurement (not the variable type) for each of the two variables.

Variable 1: Prospect for future investment

ORDINAL

Variable 2: Growth strategy

NOMINAL

(b) Below is a completed cross tabulation total count table.

TABLE: COUNT Do you have a Growth Strategy?

Prospect for future investment Neither low nor Low high

High

Grand Total

No

17

12

11

40

Yes

20

30

54

104

Grand Total

37

42

65

144

Complete the following percent of row (row percentage) cross tabulation.

TABLE: % Rows Do you have a Growth Strategy?

Prospect for future investment Neither low nor high Low

High

Grand Total

No

42.5%

30.0%

27.5%

100.00%

Yes

19.2%

28.8%

51.9%

100.00%

Grand Total

25.7%

29.2%

45.1%

100.00%

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MIS171 Business Analytics

Sample Exam 1

(c) Is there a relationship evident between a business’s belief in their ‘prospect for future investment’ and whether or not they have a ‘growth strategy’? Explain using key figures from your analysis above.

Yes, there does appear to be a relationship. If P(A|B) ≠ P(A) then dependence is evident. Thus as: P(A1|B1) = P(Low|No) = 17/40 = 42.5%

and as

P(A2|B2) = P(Low|Yes) = 20/104 = 19.2%

and as

P(A) = P(Low) = 37/144 = 25.7% And 42.5% ≠ 19.2% ≠ 25.7% dependence is evident (OR SIMILAR EXAMPLE) That is, a relationship appears to be evident between growth strategy and future investment. With businesses with a growth strategy, more likely to believe there is a ‘high’ prospect for future investment (51.9% of them). Similarly, businesses without a growth strategy, are more likely to believe there is a ‘low’ prospect for future investment (42.5% of them). OR Businesses with a growth strategy are more likely to think prospects for future investment are high. 51.9% of businesses that do have a growth strategy think that their prospect for future investment are high, yet only 27.5% of businesses without a growth strategy think the same way. On the other hand, 42.5% of businesses without a growth strategy think their prospect for future investment is low compared to only 19.5% of businesses that do have a growth strategy thinking the same way.

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MIS171 Business Analytics

Sample Exam 1

QUESTION 4 (a) Within the Bendigo regions businesses, a linear the relationship is evident between Gross Revenue ($’000) and how many employees a business has. The summary statistics for this regression model are presented below.

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations

0.99 0.98 0.98 927.82 100

ANOVA df Regression Residual Total

Intercept ACTUALNumberEmployees

1 98 99

SS MS F Significance F 3336498399 3336498399 3875.843269 1.31608E-80 84362761.96 860844.5098 3420861161

Coefficients Standard Error -111.71 105.04 101.52 1.63

t Stat -1.06 62.26

P-value 0.29 0.00

(i) From the summary output, write down the regression equation and predict the gross Revenue ($’000) for a business with 50 employees..

Gross Revenue ($’000) = 101.52*ACTUALNumberEmployees – 111.71 101.52*50-111.71 = 4964.29 = $4,964,290

(ii) Using the regression summary output above,give a practical interpretation of

•

the coefficient b1 (coefficient for ACTUALNumberEmployees) in your regression equation.

b1 = 101.52. = On average, for every extra employee a business hires, its gross revenue increases by $101,520. •

the coefficient b0 (the intercept) in your regression equation.

b0 = -111.71 = This is a nonsensical interpretation as there is no negative revenue even when a business starts with no employees.

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MIS171 Business Analytics •

Sample Exam 1

the coefficient of determination (R2).

98% of the variation in gross revenue can be explained by or attributed to the variation in how many employees a business has (or ...can be explained by the model). The remaining 2% would be explained by other factors not included in the model. Thus, this is a very strong model in explaining the variation in gross revenue. •

the standard error of the estimate (Svx).

On average, the error we will make when using the model to predict gross revenue is $927,820. b) The following is a Time Series plot for the housing approvals in Australia from October 2007 to September 2011.

i.

Describe the monthly pattern that is evident in the data

The amount of housing approvals in January tend to be the lowest in a year, while housing approval in October and November tend to be the highest in a year (roughly).

i.

Comment on the trend component

A stationary time series

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MIS171 Business Analytics

Sample Exam 1

QUESTION 5 a) Dog Chow purchases animal bones from the abattoir each day for $13/kg and sells them for $25/kg as Doggy Mc Dog Snax. Sometimes the bones cannot be used immediately by Dog Chow and are sold to a fertiliser company (for $4/kg) to make “blood and bone”, a high quality fertiliser. Based on historical data, the probability of various levels of demand for Doggy McDog Snax is as follows: Demand (for animal bones) 400 600 800

Probability 0.20 0.35 0.45

For each purchasing option, the profit or loss is calculated and summarised as follows:

i.

Probability

0.20

0.35

0.45

Demand

400

600

800

Purchase 400

4800

4800

4800

Purchase 600

3000

7200

7200

Purchase 800

1200

5400

9600

Calculate and complete the two missing entries in the above payoff table

Purchase 600 with demand at 600 = 600*-13+600*25 = 7200 Purchase 800 with demand at 600 = 800*-13+600*25+200*4 = 5400 ii.

What would be your recommendation under MaxiMax option?

Purchase 400 = 4800 Purchase 600 =7200 Purchase 800= 9600 -> Maximax recommendation

iii.

What would be your recommendation under MaxiMin option?

Purchase 400 = 4800 -> MaxMin recommendation Purchase 600 =3000 Purchase 800= 1200

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MIS171 Business Analytics

iv.

Sample Exam 1

Calculate expected values to determine which purchasing option to adopt to achieve the maximum expected profit. Show your workings.

Expected (Purchase 400) = 0.2*4800+0.35*4800+0.45*4800 = $4,800 Expected (Purchase 600) = 0.2*3000+0.35*7200+0.45*7200 = $6,360 Expected (Purchase 800) = 0.2*1200+0.35*5400+0.45*9600 = $6,450 Purchasing 800 kg will, on average, maximise profit.

b) The number of years of formal education for people in the primary industry sector of the Bendigo shire is normally distributed with a mean (µ) of 10 years and a standard deviation (σ) of 2 years. i.

What proportion of people in this primary industry sector will have less than six (6) years of formal education?

P(X1)=1-0.8413=0.1587 or 15.87% (c)

What proportion of people in this primary industry sector will have between seven (7) years and twelve (12) years of formal education?

P(X>7)=P((7-10)/2...