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January 2022 term · Business Analytics · BSMS2002

Business Analytics End Term: 3 April 2022 (January 2022 term)

The IIT Madras BS Business Analytics (Business Analytics) End Term paper sat on 3 Apr 2022, in the January 2022 term: 33 questions for 110 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.

Questions
33
Marks
110
Duration
180 min
MCQ
11
Numerical
14
MSQ
8
Take as mock testPractise with answers

Updated

Official paper: IIT M FOUNDATION DIPLOMA ENDTERM AN1 3 Apr 2022 · No negative marking.

Question 1

+1 markOne correct option

Suppose you conduct a chi-squared test of independence on the categorical variables cities and brand preferences at the significance level of 0.05. You obtain a p-value of 0.03. What will you conclude?

  1. A

    Reject the null hypothesis and conclude that the categorical variables are independent

  2. B

    Reject the null hypothesis and conclude that the categorical variables are not independent

  3. C

    Fail to reject the null hypothesis and conclude that the categorical variables are independent

  4. D

    Fail to reject the null hypothesis and conclude that the categorical variables are not independent

Show answer

Correct answer

  • B

    Reject the null hypothesis and conclude that the categorical variables are not independent

Question 1 on its own page

Question 2

+2 marksNumerical answer

You have estimated the demand to follow the following relationship: D(p)= 100−5*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*?
NOTE: Enter your answer in one decimal place.

Show answer

Correct answer: 10 (accepted within ±0.1)

Question 2 on its own page

Question 3

+5 marksNumerical answer

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?
NOTE: Enter your answer to the nearest integer.

Show answer

Correct answer: 8430 (accepted within ±10)

Question 3 on its own page

Question 4

+5 marksNumerical answer

In a multiple linear regression with 4 explanatory variables, you find that R-squared value is 0.74. The number of observations is 25. What is the value of adjusted R-squared?
NOTE: Enter your answer in two decimal places.

Show answer

Correct answer: 0.7 (accepted within ±0.04)

Question 4 on its own page

Question 5

+5 marksNumerical answer

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 linear regression with quantity as the dependent variable and other variables as independent variables and obtain an R-squared of 0.5. What is the VIF for the variable quantity?
NOTE: Enter your answer in one decimal place.

Show answer

Correct answer: 2 (accepted within ±0.1)

Question 5 on its own page

Question 6

+4 marksNumerical answer

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? NOTE: Enter your answer in two decimal places.

Show answer

Correct answer: 0.42 (accepted within ±0.02)

Question 6 on its own page

Question 7

+4 marksNumerical answer

The price of an envelop was Rs. 3/ piece yesterday and Aditya bought 10 envelopes. Today, the price is Rs. 3.75/ piece and Aditya is willing to buy only 8 envelopes. What is the elasticity of Aditya’s demand?
NOTE: Enter your answer in one decimal place.

Show answer

Correct answer: 0.8

Question 7 on its own page

Question 8

+2 marksOne or more correct options

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 0.9 and the business unit 7 has obtained an efficiency of 1 with the optimal weights of business unit 5. Which of the following statements are correct?

Select all that apply.

  1. A

    Business unit 3 may be inefficient

  2. B

    Business unit 3 will be efficient

  3. C

    Business unit 7 may be inefficient

  4. D

    Business unit 7 will be efficient

Show answer

Correct answers

  • A

    Business unit 3 may be inefficient

  • D

    Business unit 7 will be efficient

Question 8 on its own page

Question 9

+2 marksOne or more correct options

The table below provides the summary statistic for a random variable. Then what distribution could be a good fit for this random variable? (select all that is/are applicable)

Summary StatisticValue
Number of observations300
Mean12
Median13
Mode12
Std. Deviation2
Minimum11
Maximum15
Skewness0.01

Select all that apply.

  1. A

    Poisson distribution

  2. B

    Standard normal distribution

  3. C

    Uniform distribution

  4. D

    Exponential distribution

Show answer

Correct answer

  • C

    Uniform distribution

Question 9 on its own page

Question 10

+2 marksOne or more correct options

A distribution is left tailed if (select all that is applicable)

Select all that apply.

  1. A

    Coefficient of variation is positive

  2. B

    Skewness is positive

  3. C

    Skewness is negative

  4. D

    Cannot say without the histogram

Show answer

Correct answer

  • C

    Skewness is negative

Question 10 on its own pageAlso asked in Quiz 1 16 Jul 2023

Question 11

+3 marksOne or more correct options

There are 4 business units. Using the DEA, you solve the LP for all four business units and find the efficiencies for these units. The efficiency is denoted by E. For these units, E1 = 0.83, E2 = 1, E3 = 1, E4 = 0.91. Which of these units are efficient?

Select all that apply.

  1. A

    1

  2. B

    2

  3. C

    3

  4. D

    4

Show answer

Correct answers

  • B

    2

  • C

    3

Question 11 on its own page

Question 12

+3 marksOne or more correct options

A cricket analyst is interested in comparing two bowlers (X and Y) based on the number of fours conceded by them in a match. Given that both bowlers have bowled their full quota of 4 overs in a 20 over match, which of the following graphs would be the best to identify that Bowler-X has performed better than Bowler-Y (choose all that is applicable)

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • A
Question 12 on its own page

Question 13

+4 marksOne or more correct options

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 to the decision variables. After solving the linear program, you find that the first constraint is not binding (lhs < rhs) and the second constraint is binding (lhs = rhs). Which of the following statements are correct?

Select all that apply.

  1. A

    There are three decision variables in the dual

  2. B

    The dual variable corresponding to the second constraint is zero

  3. C

    There are two decision variables in the dual

  4. D

    The dual variable corresponding to the second constraint is non-zero

Show answer

Correct answers

  • C

    There are two decision variables in the dual

  • D

    The dual variable corresponding to the second constraint is non-zero

Question 13 on its own page

Question 14

+4 marksOne or more correct options

Which of the following is not a standard format used for collecting data in order to perform the conjoint analysis?

Select all that apply.

  1. A

    Ranking

  2. B

    Pairwise preferences

  3. C

    Rating

  4. D

    None of these

Show answer

Correct answer

  • D

    None of these

Question 14 on its own page

Question 15

+4 marksOne or more correct options

Correctly interpret the terms from the regression equation below:
Demand = 5843 - 158 × Price

Select all that apply.

  1. A

    5483 is the demand when price is zero

  2. B

    if the price is increased by 1 Rs, demand will reduce by 158 unit

  3. C

    158 is the demand when price is zero

  4. D

    if the price is increased by 1 Rs, demand will reduce by 5843 units

Show answer

Correct answers

  • A

    5483 is the demand when price is zero

  • B

    if the price is increased by 1 Rs, demand will reduce by 158 unit

Question 15 on its own page

Question 16

+4 marksOne correct option

What is the purpose of doing a conjoint analysis?

  1. A

    To find the attribute values for an ideal product

  2. B

    To understand the importance of each attribute from the customer’s point of view

  3. C

    To find the attribute values for an ideal product & To understand the importance of each attribute from the customer’s point of view

  4. D

    None of these

Show answer

Correct answer

  • C

    To find the attribute values for an ideal product & To understand the importance of each attribute from the customer’s point of view

Question 16 on its own page

Question 17

+4 marksOne correct option

For 4 options (4 products) and 2 attributes conjoint problem, how many pairwise options will the customer have? Example: (1,2) says that option one is preferred over 2 & (1,3)

  1. A

    4

  2. B

    12

  3. C

    8

  4. D

    6

Show answer

Correct answer

  • D

    6

Question 17 on its own page

Question 18

+4 marksOne correct option

In the pairwise comparison, which of the following is true:

  1. A

    We want to minimize the violation with regard to wrong preferences

  2. B

    Objective function is to maximize the goodness of fit

  3. C

    We want to minimize the violation with regard to wrong preferences & Objective function is to maximize the goodness of fit

  4. D

    We neither want to minimize the violation with regard to wrong preferences nor the Objective function is to maximize the goodness of fit

Show answer

Correct answer

  • C

    We want to minimize the violation with regard to wrong preferences & Objective function is to maximize the goodness of fit

Question 18 on its own page

Question 19

+4 marksOne correct option

What is the satiating price for a Constant-elasticity price response function?

  1. A

    Zero

  2. B

    Does not exist

  3. C

    Equal to the Market size (D0)

  4. D

    Can be anything

Show answer

Correct answer

  • B

    Does not exist

Question 19 on its own page

Question 20

+4 marksOne correct option

Correctly identify the description for the regions depicted as "A" and "B" in the picture below from the given options

  1. A

    A: Latent Demand, B: Consumer Surplus

  2. B

    B: Latent Demand, A: Consumer Surplus

  3. C

    A: Latent Demand, B: Seller Surplus

  4. D

    None of these

Show answer

Correct answer

  • A

    A: Latent Demand, B: Consumer Surplus

Question 20 on its own page

Question 21

+5 marksOne correct option

A customer is trying to choose between two products O1 and O2. In the diagram below, points O1, O2 represent the coordinates of the two products on two attributes. “X” represents the coordinates of the ideal product. Which of the following are true?

  1. A

    Customers will prefer O1 when d2>d1

  2. B

    Customers will prefer O2 when d1<d2

  3. C

    Customers will prefer O1 when d2>d1 & Customers will prefer O2 when d1<d2

  4. D

    Customers will not prefer O1 when d2>d1 & Customers will not prefer O2 when d1<d2

Show answer

Correct answer

  • A

    Customers will prefer O1 when d2>d1

Question 21 on its own page

Question 22

+2 marksOne correct option

How do we capture the latent demand?

  1. A

    Increasing price

  2. B

    Reducing price

  3. C

    Both Increasing and Reducing price

  4. D

    None of these

Show answer

Correct answer

  • B

    Reducing price

Question 22 on its own page

Question 23

+3 marksOne correct option

The daily sales of choco-chip ice-creams in an ice-cream parlour is assumed to follow a Normal distribution with a mean of 5 and a variance of 4. To check the assumption of normal distribution, the sales of choco-chip ice-creams at the ice-cream parlour for 7 days was collected (Table-1). On all 7 days, the total number of ice-creams (of all flavours) sold per day was 100. With this data, answer the given subquestions.
{Note: Round all your calculations (intermediate and final) to one decimal place}

DayThe actual number of choco-chip ice-creams sold
Day-112
Day-214
Day-312
Day-413
Day-512
Day-611
Day-712

Table-1

For the given data in Table-1. What is the expected number of choco-chip ice-creams that are sold on Day-2?

  1. A

    5

  2. B

    14

  3. C

    12.3

  4. D

    14.3

Show answer

Correct answer

  • C

    12.3

Question 23 on its own page

Question 24

+5 marksNumerical answer

The daily sales of choco-chip ice-creams in an ice-cream parlour is assumed to follow a Normal distribution with a mean of 5 and a variance of 4. To check the assumption of normal distribution, the sales of choco-chip ice-creams at the ice-cream parlour for 7 days was collected (Table-1). On all 7 days, the total number of ice-creams (of all flavours) sold per day was 100. With this data, answer the given subquestions.
{Note: Round all your calculations (intermediate and final) to one decimal place}

DayThe actual number of choco-chip ice-creams sold
Day-112
Day-214
Day-312
Day-413
Day-512
Day-611
Day-712

Table-1

What is the value for the Chi-Square Goodness of Fit Test statistic?

Show answer

Correct answer: 0.4 (accepted within ±0.1)

Question 24 on its own page

Question 25

+3 marksNumerical answer

The daily sales of choco-chip ice-creams in an ice-cream parlour is assumed to follow a Normal distribution with a mean of 5 and a variance of 4. To check the assumption of normal distribution, the sales of choco-chip ice-creams at the ice-cream parlour for 7 days was collected (Table-1). On all 7 days, the total number of ice-creams (of all flavours) sold per day was 100. With this data, answer the given subquestions.
{Note: Round all your calculations (intermediate and final) to one decimal place}

DayThe actual number of choco-chip ice-creams sold
Day-112
Day-214
Day-312
Day-413
Day-512
Day-611
Day-712

Table-1

How many degrees of freedom does that Chi-Square Goodness of Fit Test statistic have?

Show answer

Correct answer: 4

Question 25 on its own page

Question 26

+1 markOne correct option

The daily sales of choco-chip ice-creams in an ice-cream parlour is assumed to follow a Normal distribution with a mean of 5 and a variance of 4. To check the assumption of normal distribution, the sales of choco-chip ice-creams at the ice-cream parlour for 7 days was collected (Table-1). On all 7 days, the total number of ice-creams (of all flavours) sold per day was 100. With this data, answer the given subquestions.
{Note: Round all your calculations (intermediate and final) to one decimal place}

DayThe actual number of choco-chip ice-creams sold
Day-112
Day-214
Day-312
Day-413
Day-512
Day-611
Day-712

Table-1

Which of the following is the correct null hypothesis for the Goodness of fit test for this problem (with data in Table-1)?

  1. A

    The distribution of sale of choco-chip ice-creams at the ice-cream parlour is normal

  2. B

    The distribution of sale of choco-chip ice-creams is normal

  3. C

    The distribution of choco-chip ice-creams at the ice-cream parlour is normal

  4. D

    The distribution of choco-chip ice-creams is normal

Show answer

Correct answer

  • A

    The distribution of sale of choco-chip ice-creams at the ice-cream parlour is normal

Question 26 on its own page

Question 27

+2 marksNumerical answer

The health parameters of 100 patients are used to develop a logistic model that predicts if a given patient has CORONA (Y=1) or not (Y=0). It is seen that the model correctly predicts the presence of CORONA in 23 patients and correctly predicted the absence of CORONA in 11 patients. The threshold set to obtain these results was 0.6, and the variable of focus was to identify the patients with CORONA (Y=1). Then answer the given subquestions

What is the accuracy (in percentage) of predicting CORONA patients correctly? (round to two decimal places)

Show answer

Correct answer: 16.955 (accepted within ±0.055)

Question 27 on its own page

Question 28

+2 marksNumerical answer

The health parameters of 100 patients are used to develop a logistic model that predicts if a given patient has CORONA (Y=1) or not (Y=0). It is seen that the model correctly predicts the presence of CORONA in 23 patients and correctly predicted the absence of CORONA in 11 patients. The threshold set to obtain these results was 0.6, and the variable of focus was to identify the patients with CORONA (Y=1). Then answer the given subquestions

The number of data points that contribute to the “Type-1 Error” of the model is ___________ NOTE: Enter your answer to the nearest integer.

Show answer

Correct answer: 77

Question 28 on its own page

Question 29

+2 marksNumerical answer

The health parameters of 100 patients are used to develop a logistic model that predicts if a given patient has CORONA (Y=1) or not (Y=0). It is seen that the model correctly predicts the presence of CORONA in 23 patients and correctly predicted the absence of CORONA in 11 patients. The threshold set to obtain these results was 0.6, and the variable of focus was to identify the patients with CORONA (Y=1). Then answer the given subquestions

With what precision (in percentage) are patients without CORONA identified by the model? (round to two decimal places)

Show answer

Correct answer: 13 (accepted within ±0.5)

Question 29 on its own page

Question 30

+4 marksNumerical answer

Given the below regression output, calculate the cell values highlighted in yellow:

SUMMARY OUTPUT

Regression Statistics
Multiple R0.856678246
R Square0.733897617
Adjusted R Square0.724721673
Standard Error1290.44820879.98060985
Observations31

ANOVA

dfSSMSFSignificance F
Regression1133188236.7133188236.7Q37.80618E-10
ResidualQ148292440.76Q2
Total30181480677.4
CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%
Intercept5842.836198400.683778914.582163066.94552E-155023.3458566662.3265395023.3458566662.326539
Price-157.700873917.63363083-8.9431879027.80618E-10-193.7656983-121.6360494-193.7656983-121.6360494

Based on the above data, answer the given subquestions.

What is the value of Q1?
NOTE: Enter your answer to the nearest integer.

Show answer

Correct answer: 29

Question 30 on its own page

Question 31

+4 marksNumerical answer

Given the below regression output, calculate the cell values highlighted in yellow:

SUMMARY OUTPUT

Regression Statistics
Multiple R0.856678246
R Square0.733897617
Adjusted R Square0.724721673
Standard Error1290.44820879.98060985
Observations31

ANOVA

dfSSMSFSignificance F
Regression1133188236.7133188236.7Q37.80618E-10
ResidualQ148292440.76Q2
Total30181480677.4
CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%
Intercept5842.836198400.683778914.582163066.94552E-155023.3458566662.3265395023.3458566662.326539
Price-157.700873917.63363083-8.9431879027.80618E-10-193.7656983-121.6360494-193.7656983-121.6360494

Based on the above data, answer the given subquestions.

What is the value of Q2?
NOTE: Enter your answer to the nearest integer.

Show answer

Correct answer: 1665256 (accepted within ±1)

Question 31 on its own page

Question 32

+4 marksNumerical answer

Given the below regression output, calculate the cell values highlighted in yellow:

SUMMARY OUTPUT

Regression Statistics
Multiple R0.856678246
R Square0.733897617
Adjusted R Square0.724721673
Standard Error1290.44820879.98060985
Observations31

ANOVA

dfSSMSFSignificance F
Regression1133188236.7133188236.7Q37.80618E-10
ResidualQ148292440.76Q2
Total30181480677.4
CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%
Intercept5842.836198400.683778914.582163066.94552E-155023.3458566662.3265395023.3458566662.326539
Price-157.700873917.63363083-8.9431879027.80618E-10-193.7656983-121.6360494-193.7656983-121.6360494

Based on the above data, answer the given subquestions.

What is the value of Q3?
NOTE: Enter your answer to the nearest integer.

Show answer

Correct answer: 79.5 (accepted within ±2.5)

Question 32 on its own page

Question 33

+3 marksOne correct option

Given the below regression output, calculate the cell values highlighted in yellow:

SUMMARY OUTPUT

Regression Statistics
Multiple R0.856678246
R Square0.733897617
Adjusted R Square0.724721673
Standard Error1290.44820879.98060985
Observations31

ANOVA

dfSSMSFSignificance F
Regression1133188236.7133188236.7Q37.80618E-10
ResidualQ148292440.76Q2
Total30181480677.4
CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%
Intercept5842.836198400.683778914.582163066.94552E-155023.3458566662.3265395023.3458566662.326539
Price-157.700873917.63363083-8.9431879027.80618E-10-193.7656983-121.6360494-193.7656983-121.6360494

Based on the above data, answer the given subquestions.

What is the conclusion from the given result?

  1. A

    Accept the Null Hypothesis

  2. B

    Reject the Null Hypothesis

  3. C

    P-value cannot be found

  4. D

    Cannot say insufficient data

Show answer

Correct answer

  • B

    Reject the Null Hypothesis

Question 33 on its own page