The IIT Madras BS Business Analytics (Business Analytics) End Term paper sat on 7 Aug 2022, in the May 2022 term, set QPD1: 27 questions for 55 marks in 180 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.
A leading European two-wheeler manufacturer is trying to build an ideal scooter for the Indian market. Which of the following tools will help him understand: how important the attributes such as Engine Capacity, LED Lights, Fuel Efficiency, and Smart Connect Technology are to the customers?
Data Envelopment Analysis
Conjoint Analysis
Chi-Square test
Both Data Envelopment Analysis & Chi-Square test
Correct answer
Conjoint Analysis
Suppose you conduct a chi-squared test of independence on the categorical variables cities and brand preferences at the significance level 0.1. You obtain a p-value of 0.05. What will you conclude?
Reject the null hypothesis and conclude that the categorical variables are independent
Reject the null hypothesis and conclude that the categorical variables are not independent
Fail to reject the null hypothesis and conclude that the categorical variables are independent
Fail to reject the null hypothesis and conclude that the categorical variables are not independent
Correct answer
Reject the null hypothesis and conclude that the categorical variables are not independent
There are 4 business units. Using the DEA, you solve the LP for all the four business units and find the efficiencies for these units. The efficiency is denoted by E. For these units, E1 = 0.92, E2 = 0.89, E3 = 1, E4 = 0.91. Which of these units are efficient?
1
2
3
4
Correct answer
3
Which of the following is not a form of conjoint analysis?
Choice based
Adaptive based
Full profile
Selective attribute type
Menu-based
Correct answer
Selective attribute type
In a conjoint problem with 4 products and 2 attributes, how many pair-wise preferences are possible?
8
6
16
12
Correct answer
6
Let’s say a customer wants to buy a car and has 3 brands to choose from; 2 engine options; and 3 type of gear boxes. How many options will the customer rate or rank for performing the conjoint analysis?
18
27
54
72
Correct answer
18
Say a data is distributed as “Normal” with a right tail. If it is compared with an “Symmetric Normal” distribution, then which of the following states is/ are true (choose all that is applicable)
In a “P-P plot”, the data will fall on a line which is indicate at 45-degree to the X- axis
In a “Q-Q plot”, the data will fall on a line which is indicate at 45-degree to the X-axis
In a “P-P plot”, the data will not entirely fall on a line which is indicate at 45- degree to the X-axis
In a “Q-Q plot”, the data will not entirely fall on a line which is indicate at 45- degree to the X-axis
Cannot use P-P plot or Q-Q plot as the assumed distribution is discrete
Correct answers
In a “Q-Q plot”, the data will fall on a line which is indicate at 45-degree to the X-axis
In a “P-P plot”, the data will not entirely fall on a line which is indicate at 45- degree to the X-axis
There are 7 business units and you are using the DEA to compare them. You solve the LP for business unit 5. You find from the constraint expression that the business unit 3 has obtained an efficiency of 0.8 and the business unit 7 has obtained an efficiency of 0.9 with the optimal weights of business unit 5. Which of the following statements are correct?
Business unit 3 may be inefficient
Business unit 3 will be efficient
Business unit 7 may be inefficient
Business unit 7 will be efficient
Correct answers
Business unit 3 may be inefficient
Business unit 7 may be inefficient
What is the format of data needed for performing the conjoint analysis using the Statistical or Linear Regression Approach?
Consumer Choice Data is Ranking or Ratings
Consumer Choice Data is Pairwise Comparison
Value of the attributes are continuous
Value of the product attributes are categorical
Correct answers
Consumer Choice Data is Ranking or Ratings
Value of the product attributes are categorical
You have estimated the demand to follow the following relationship: D(p)=100 - 20*p. Now, you intend to maximize the revenue R(p)= D(p)*p. You find the first derivative of R(p) with respect to p, equate it to 0 and find p^(*). What is the value of p^(*)?
Correct answer: 2.5 (accepted within ±0.1)
In a multiple linear regression with 3 explanatory variables, you find that R-squared value is 0.75. The number of observations is 25. What is the value of adjusted R-squared?
Correct answer: 0.71 (accepted within ±0.05)
You are conducting a multiple linear regression with sales as the dependent variable. Price, quantity and rating score are the independent variables. In the multiple linear regression, you find that the direct effect of price on sales is 0.3, the direct effect of quantity on sales is 0.2 and the direct effect of rating score on sales is 0.4. And, you also know that the effect of price on quantity is 0.2 and the effect of price on rating score is 0.1. What is the total effect of price on sales?
Correct answer: 0.38 (accepted within ±0.02)
You solve the primal of a linear program with maximization objective, three decision variables and two constraints of the less than or equal to type. Non-negativity restrictions apply on the decision variables. After solving the linear program, you find that the first constraint is not binding (lhs < rhs) and the second constraint is not binding (lhs < rhs). Which of the following statements are correct?
There are three decision variables in the dual
The dual variable corresponding to the first constraint is zero
There are four decision variables in the dual
The dual variable corresponding to the second constraint is zero
Correct answers
The dual variable corresponding to the first constraint is zero
The dual variable corresponding to the second constraint is zero
There are 6 business units. There are two outputs and one input under consideration. You are solving the optimization problem for business unit 3 and find that the efficiency is 0.7. You find that the dual variables corresponding to the constraints of business units 4 and 5 are non-zero and the dual variables corresponding to the constraints of other units are zero. The dual variables corresponding to the constraints of business units 4 and 5 are 0.3 and 0.4 respectively. You are given the following table where sales and number of leads are the two outputs.
What is the sales in HCU 3?
Correct answer: 8330 (accepted within ±5)
You are conducting a multiple linear regression with sales as the dependent variable. Price, quantity and rating score are the independent variables. In order to calculate the VIF for the variable quantity, you implement a linear regression with quantity as the dependent variable and other variables as independent variables and obtain R-squared of 0.6. What is the VIF for the variable quantity?
Correct answer: 2.5 (accepted within ±0.1)
Ms. X is working is with the data given in Table-1 below. Using this information answer the given subquestions
| Sales of a Product in a City for a given Year | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Product | City-1 (1990) | City-2 (1990) | City-3 (1990) | City-1 (1991) | City-2 (1991) | City-3 (1991) | City-1 (1992) | City-2 (1992) | City-3 (1992) |
| A | 100 | 90 | 250 | 120 | 50 | 120 | 140 | 20 | 500 |
| B | 145 | 300 | 500 | 175 | 250 | 250 | 195 | 230 | 1000 |
| C | 90 | 180 | 30 | 100 | 110 | 15 | 110 | 95 | 58 |
| D | 130 | 220 | 132 | 140 | 200 | 61 | 150 | 180 | 270 |
Table-1
If X wants visualize how the sales of a product has changed over the years in the different cities, then which visualization would be most appropriate?
Line graph for each product’s sales over the years for each city
Line graph for each city’s sale over the years for each product
Line graph for each year’s sale for every product in each city
Pie chart for each product’s sales in the year 1992 for each city
Pie chart for each city’s sales in the year 1992
The given table data with columns re-arranged as specified below
Correct answer
Line graph for each product’s sales over the years for each city
Ms. X is working is with the data given in Table-1 below. Using this information answer the given subquestions
| Sales of a Product in a City for a given Year | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Product | City-1 (1990) | City-2 (1990) | City-3 (1990) | City-1 (1991) | City-2 (1991) | City-3 (1991) | City-1 (1992) | City-2 (1992) | City-3 (1992) |
| A | 100 | 90 | 250 | 120 | 50 | 120 | 140 | 20 | 500 |
| B | 145 | 300 | 500 | 175 | 250 | 250 | 195 | 230 | 1000 |
| C | 90 | 180 | 30 | 100 | 110 | 15 | 110 | 95 | 58 |
| D | 130 | 220 | 132 | 140 | 200 | 61 | 150 | 180 | 270 |
Table-1
If Ms. X has created the below visualization (Figure-1) for the data of product-A in Table-1. What is the primary message that is conveyed through this?
City-3 has the highest sales for the product-A in the current year
The sales of Product-A is constantly fluctuating over the years
The sales of Product-A is drastically different across cities in any given year
The sales of product-A in city-2 is lowest among all the cities in any given year
None of these
Correct answer
The sales of product-A in city-2 is lowest among all the cities in any given year
Ms. X is working is with the data given in Table-1 below. Using this information answer the given subquestions
| Sales of a Product in a City for a given Year | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Product | City-1 (1990) | City-2 (1990) | City-3 (1990) | City-1 (1991) | City-2 (1991) | City-3 (1991) | City-1 (1992) | City-2 (1992) | City-3 (1992) |
| A | 100 | 90 | 250 | 120 | 50 | 120 | 140 | 20 | 500 |
| B | 145 | 300 | 500 | 175 | 250 | 250 | 195 | 230 | 1000 |
| C | 90 | 180 | 30 | 100 | 110 | 15 | 110 | 95 | 58 |
| D | 130 | 220 | 132 | 140 | 200 | 61 | 150 | 180 | 270 |
Table-1
Say you want to see if the distribution of sales of Product-A in the Table-1 follows a uniform distribution within the range of 0 to 300 when split into bins as specified in Table-2. Then what is the expected frequency in any given bin (round your answer to two decimal places)?
| Bin Number | Bin Range |
|---|---|
| Bin-1 | Sales value less than or equal to 50 |
| Bin-2 | Sales value greater than 50 but less than or equal to 100 |
| Bin-3 | Sales value greater than 100 but less than or equal to 150 |
| Bin-4 | Sales value greater than 150 but less than or equal to 200 |
| Bin-5 | Sales value greater than 200 but less than or equal to 250 |
| Bin-6 | Sales value greater than 250 but less than or equal to 300 |
Table-2
Correct answer: 1.5
Ms. X is working is with the data given in Table-1 below. Using this information answer the given subquestions
| Sales of a Product in a City for a given Year | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Product | City-1 (1990) | City-2 (1990) | City-3 (1990) | City-1 (1991) | City-2 (1991) | City-3 (1991) | City-1 (1992) | City-2 (1992) | City-3 (1992) |
| A | 100 | 90 | 250 | 120 | 50 | 120 | 140 | 20 | 500 |
| B | 145 | 300 | 500 | 175 | 250 | 250 | 195 | 230 | 1000 |
| C | 90 | 180 | 30 | 100 | 110 | 15 | 110 | 95 | 58 |
| D | 130 | 220 | 132 | 140 | 200 | 61 | 150 | 180 | 270 |
Table-1
If a Chi-Square Goodness-Of-Fit Test to check if the data for Product-A in Table-1 follows a Uniform Distribution with bins as specified in Table-2, then what is the value of the Test statistic (round your answer to two decimal places)?
{Hint: Chi-square = }
Correct answer: 3.6 (accepted within ±0.1)
Ms. X is working is with the data given in Table-1 below. Using this information answer the given subquestions
| Sales of a Product in a City for a given Year | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Product | City-1 (1990) | City-2 (1990) | City-3 (1990) | City-1 (1991) | City-2 (1991) | City-3 (1991) | City-1 (1992) | City-2 (1992) | City-3 (1992) |
| A | 100 | 90 | 250 | 120 | 50 | 120 | 140 | 20 | 500 |
| B | 145 | 300 | 500 | 175 | 250 | 250 | 195 | 230 | 1000 |
| C | 90 | 180 | 30 | 100 | 110 | 15 | 110 | 95 | 58 |
| D | 130 | 220 | 132 | 140 | 200 | 61 | 150 | 180 | 270 |
Table-1
A Chi-squared Goodness-Of-Fit test with the bins as specified in Table-2 is going to be carried out to check if the data on sales (whole data in Table-1) is normal or not. Then what is the degrees of freedom for the test?
Correct answer: 3
A logistic model has been fit for a data set with the goal to predict the positive class (Y=1). The confusion matrix obtained for this model on the test dataset is provided in Table-3. Using this, answer the given subquestions
How many “True Positives” is the model predicting?
Correct answer: 11
A logistic model has been fit for a data set with the goal to predict the positive class (Y=1). The confusion matrix obtained for this model on the test dataset is provided in Table-3. Using this, answer the given subquestions
How many “False Positives” is the model predicting?
Correct answer: 77
A logistic model has been fit for a data set with the goal to predict the positive class (Y=1). The confusion matrix obtained for this model on the test dataset is provided in Table-3. Using this, answer the given subquestions
How many “True Negatives” is the model predicting?
Correct answer: 23
A logistic model has been fit for a data set with the goal to predict the positive class (Y=1). The confusion matrix obtained for this model on the test dataset is provided in Table-3. Using this, answer the given subquestions
How many “False Negatives” is the model predicting?
Correct answer: 45
A logistic model has been fit for a data set with the goal to predict the positive class (Y=1). The confusion matrix obtained for this model on the test dataset is provided in Table-3. Using this, answer the given subquestions
What is the accuracy for the model (enter only the numerical value in percentage, without the “%” symbol and round it to two decimal places)?
Correct answer: 21.5 (accepted within ±0.5)
A logistic model has been fit for a data set with the goal to predict the positive class (Y=1). The confusion matrix obtained for this model on the test dataset is provided in Table-3. Using this, answer the given subquestions
What is the recall for the model when predicting the negative class (enter only the numerical value in percentage, without the “%” symbol and round it to two decimal places)?
Correct answer: 23 (accepted within ±0.2)
A logistic model has been fit for a data set with the goal to predict the positive class (Y=1). The confusion matrix obtained for this model on the test dataset is provided in Table-3. Using this, answer the given subquestions
What is the precision for the model when predicting the positive class (enter only the numerical value in percentage, without the “%” symbol and round it to two decimal places)?
Correct answer: 12.5 (accepted within ±0.5)
