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ISYS3375 Business Analytics

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Question:

SECTION A:  Discussion Questions 

  • Explain the concept of having the imbalance data in classification techniques and the way that it should be treated in developing the classification models?
  • Explain the concept of over-fitting. Explain how overfitting can be avoided?
  • Give two examples of how logistics regression can be used. You only need to explain the problem. One example is the bank that are using logistic regression to classify its new customers for loan approval. The bank wanted to identify customers that are more likely to default on their loan. Explain why you cannot use linear regression in your examples.                                                                                                         
  • SECTION B:  QUANTITATIVE QUESTIONS
  1. There are 500 client records in the first sheet of the file Toy-Info which have shopped many special toys from an e-Business website. Each record includes data on types of product purchased (between 1-5), purchase amount ($), age, gender, marital status, whether the client has a membership and whether the customer has a discount card.

A business analyst has applied the k-means clustering method on all seven variables. The analyst increased the number of clusters to recommend a proper value of k. The resultant tests for k=5 and k=6 shown in the following sheets of the file revealed the best k as k=6.

  1. Explain how the analyst found that k=6 is a proper number of clusters. Refer the relevant sheet name, table name and the values you compared.
  2. Describe all 6 clusters by their average characteristics.                                                                                                                                              (5+5=10 marks)
  3. In order to improve the overall quality of a new material, a chemist experiments with the effect of two indices (A & B) on each other in her laboratory. In the following table, the values of these indices have been captured for each experiment

No. of experiment

Index A

Index B

1

248

29915

2

247

29915

3

247

29991

4

253

29807

5

251

29965

6

230

29620

7

232

29526

8

237

29383

9

233

29345

10

242

29711

11

242

29570

12

245

29822

  1. Plot a scatter chart for this data where index A is the independent variable. What does the scatter chart indicate about the relationship between indices A and B? How strong is the relationship? Create an estimated simple regression model and write the equation?
  2. Apply and investigate a polynomial regression model that includes intercept and terms x, x^2 and x^3. Is this new model statistically significant? Is this new model better than the linear model, explain?                                                                                                                                        (9+8 = 17 marks)
  • The following data is the results of a 4- year study conducted to assess how age, weight, and gender influence the risk of diabetes. Risk is interpreted as the probability (times 100) that the patient will have diabetes over the next 4-year period.
  1. Develop a multiple regression model that relates risk of diabetes to the person’s age, weight and the gender. Present the regression formula as a mathematical equation. Interpret the coefficients of the regression and comment on the strength of the regression.
  2. Develop an estimated multiple regression model that relates risk of diabetes to the person’s age, weight, gender and life style. Present the regression formula as a mathematical equation. Interpret the coefficients of the regression and comment on the strength of the regression.
  3. What is the risk percentage of diabetes over the next 4 years for a 55-year-old man living in a big city with 70 kg weight

Age

Weight (Kg)

Gender

Life style

Risk (%)

53

78

Female

Small town

40

24

77

Male

Big city

23

77

83

Female

Country

67

88

89

Female

Small town

71

56

65

Male

Big city

45

71

82

Female

Country

54

53

79

Female

Small town

48

70

66

Male

Small town

49

80

80

Female

Big city

65

78

67

Male

Big city

59

71

69

Male

Big city

56

70

78

Female

Small town

59

67

75

Male

Country

46

77

95

Female

Big city

64

60

57

Male

Country

39

82

100

Female

Big city

73

66

85

Male

Small town

63

80

96

Male

Big city

87

62

83

Female

Country

52

59

93

Male

Big city

61


  • An internet provider company in Australia is interested in identifying the reason for individuals who are still undecided in buying the new NBN service of the company. The file NBN-service contains data on the first sheet which introduces a sample of customers with variables that tracked the decision outcome.

A business analyst has created a standard partition of the data with all tracked variables and 40% of observations in the training set, 35% in the validation set, and 25% in the test set. The analyst applied two logistic regression models to classify undecided customers of the company. The resultant output of the Solver software for both models has been added in the following sheets. 

  1. Determine the selected input variables in each model and explain why the analyst has changed one of the input variables.
  2. Write the obtained logistic regression equation for the first model shown in worksheet “4-1-1” and predict a customer with Contract duration of 16 months, Bonus data of 63 GB and Usage of 237 GB whether he/she will decide to buy the new service or not? Explain how you found the prediction.
  3. Find the class 1 and class 0 errors based on the sheet “4-1-2” and compare your results with the confusion matrix. Explain which kind of these errors are more undesirable in this model?
  4. In the second model (shown in worksheet “4-2-1”), compare the accuracy of the model with the first model. Which one do you recommend?    (3+6+7+8 = 24 marks)
  • A put option in finance allows you to sell a share of stock in the future at a given price. There are different types of put options. A European put option allows you to sell a share of stock at a given price (called the exercise price) at a particular point in time after the purchase of the option. For example, suppose you purchase an eight-month European put option for a share of stock with an exercise price of $29. If eight months later, the stock price per share is $29 or more, the option has no value. If in six months time the stock price is lower than $29 per share, then you can purchase the stock and immediately sell it at the higher exercise price of $29. If the price per share in eight months is $26.4, you can purchase a share of the stock for $26.4 and then use the put option to immediately sell the share for $29. Your profit would be the difference, $29-$26.4 = $2.6 per share, less the cost of the option. If you paid $1.5 per put option, then your profit would be $2.6-$1.5=$1.1 per share. 
  1. Build a model to calculate the profit of this European put option.
  2. Construct a data table that shows the profit per share for a share price in eight months between $15 and $35 per share in increments of $1.    (8+8 = 16 marks)
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