Business Analytics Quiz 2: 23 November 2025 (September 2025 term)

A regression model is fit on a dataset with 500 data points. The total variability (magnitude) in the dependent variable is 1,12,43,679. The final model is as specified below. The model was able to explain 87% of the variability in the dependent variable.

Given this information answer the given subquestions.

What is the adjusted R-square value for the model?
(Note: Enter the answer as a numeric percentage value rounded to two decimal places without the % symbol. For example, if your answer is “10.256 %”, enter it as “10.26”)

A regression model is fit on a dataset with 500 data points. The total variability (magnitude) in the dependent variable is 1,12,43,679. The final model is as specified below. The model was able to explain 87% of the variability in the dependent variable.

Given this information answer the given subquestions.

What is the total variability (magnitude) that is present in the error terms for this model? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)

A regression model is fit on a dataset with 500 data points. The total variability (magnitude) in the dependent variable is 1,12,43,679. The final model is as specified below. The model was able to explain 87% of the variability in the dependent variable.

Given this information answer the given subquestions.

How many degrees of freedom will be present for the “SST” term in the ANOVA table for this model?
(Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)

A regression model is fit on a dataset with 500 data points. The total variability (magnitude) in the dependent variable is 1,12,43,679. The final model is as specified below. The model was able to explain 87% of the variability in the dependent variable.

Given this information answer the given subquestions.

What is the F-statistic value for this model?
(Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)

“Milo Loner (ML)” is a bank that gives out personal loans to customers. Currently, the process of document verification is done manually by verifying the scores from 2 variables “Earnings” and “Tenure”. The aim of inspection process is to identify customers who will default on a loan (considered as the negative class). From historical experience, manual inspection correctly identifies 85% of loan defaulters in any given batch of only defaulter customers.
The top brass at ML, Dr. Milo, has embarked on a journey in business analytics. Hence, he has decided to replace the manual inspection with an Automatic Defaulter Detection System (ADDS). This ADDS runs a trained logistic model in the background which classifies an applicant as “Defaulter” or “Non-Defaulter” based on the scores for “Earnings” and “Tenure”. To test the ADDS, a sample of 200 applications are taken. The sample is imbalanced and only 30% of the sample applicants were non-defaulters. The sample applications are passed through the ADDS, and the system identifies 70% of the actual non-defaulters as defaulters and 10% of actual defaulters as non-defaulters.
Using this information, answer the given subquestions.

How many “True Positives” is ADDS predicting?

“Milo Loner (ML)” is a bank that gives out personal loans to customers. Currently, the process of document verification is done manually by verifying the scores from 2 variables “Earnings” and “Tenure”. The aim of inspection process is to identify customers who will default on a loan (considered as the negative class). From historical experience, manual inspection correctly identifies 85% of loan defaulters in any given batch of only defaulter customers.
The top brass at ML, Dr. Milo, has embarked on a journey in business analytics. Hence, he has decided to replace the manual inspection with an Automatic Defaulter Detection System (ADDS). This ADDS runs a trained logistic model in the background which classifies an applicant as “Defaulter” or “Non-Defaulter” based on the scores for “Earnings” and “Tenure”. To test the ADDS, a sample of 200 applications are taken. The sample is imbalanced and only 30% of the sample applicants were non-defaulters. The sample applications are passed through the ADDS, and the system identifies 70% of the actual non-defaulters as defaulters and 10% of actual defaulters as non-defaulters.
Using this information, answer the given subquestions.

How many “False Positives” is ADDS predicting?

“Milo Loner (ML)” is a bank that gives out personal loans to customers. Currently, the process of document verification is done manually by verifying the scores from 2 variables “Earnings” and “Tenure”. The aim of inspection process is to identify customers who will default on a loan (considered as the negative class). From historical experience, manual inspection correctly identifies 85% of loan defaulters in any given batch of only defaulter customers.
The top brass at ML, Dr. Milo, has embarked on a journey in business analytics. Hence, he has decided to replace the manual inspection with an Automatic Defaulter Detection System (ADDS). This ADDS runs a trained logistic model in the background which classifies an applicant as “Defaulter” or “Non-Defaulter” based on the scores for “Earnings” and “Tenure”. To test the ADDS, a sample of 200 applications are taken. The sample is imbalanced and only 30% of the sample applicants were non-defaulters. The sample applications are passed through the ADDS, and the system identifies 70% of the actual non-defaulters as defaulters and 10% of actual defaulters as non-defaulters.
Using this information, answer the given subquestions.

How many “True Negatives” is ADDS predicting?

“Milo Loner (ML)” is a bank that gives out personal loans to customers. Currently, the process of document verification is done manually by verifying the scores from 2 variables “Earnings” and “Tenure”. The aim of inspection process is to identify customers who will default on a loan (considered as the negative class). From historical experience, manual inspection correctly identifies 85% of loan defaulters in any given batch of only defaulter customers.
The top brass at ML, Dr. Milo, has embarked on a journey in business analytics. Hence, he has decided to replace the manual inspection with an Automatic Defaulter Detection System (ADDS). This ADDS runs a trained logistic model in the background which classifies an applicant as “Defaulter” or “Non-Defaulter” based on the scores for “Earnings” and “Tenure”. To test the ADDS, a sample of 200 applications are taken. The sample is imbalanced and only 30% of the sample applicants were non-defaulters. The sample applications are passed through the ADDS, and the system identifies 70% of the actual non-defaulters as defaulters and 10% of actual defaulters as non-defaulters.
Using this information, answer the given subquestions.

How many “False Negatives” is ADDS predicting?

“Milo Loner (ML)” is a bank that gives out personal loans to customers. Currently, the process of document verification is done manually by verifying the scores from 2 variables “Earnings” and “Tenure”. The aim of inspection process is to identify customers who will default on a loan (considered as the negative class). From historical experience, manual inspection correctly identifies 85% of loan defaulters in any given batch of only defaulter customers.
The top brass at ML, Dr. Milo, has embarked on a journey in business analytics. Hence, he has decided to replace the manual inspection with an Automatic Defaulter Detection System (ADDS). This ADDS runs a trained logistic model in the background which classifies an applicant as “Defaulter” or “Non-Defaulter” based on the scores for “Earnings” and “Tenure”. To test the ADDS, a sample of 200 applications are taken. The sample is imbalanced and only 30% of the sample applicants were non-defaulters. The sample applications are passed through the ADDS, and the system identifies 70% of the actual non-defaulters as defaulters and 10% of actual defaulters as non-defaulters.
Using this information, answer the given subquestions.

What is the accuracy of the ADDS?
(Note: Enter the answer as a numeric percentage value rounded to two decimal places without the % symbol. For example, if your answer is “10.256 %”, enter it as “10.26”)

“Milo Loner (ML)” is a bank that gives out personal loans to customers. Currently, the process of document verification is done manually by verifying the scores from 2 variables “Earnings” and “Tenure”. The aim of inspection process is to identify customers who will default on a loan (considered as the negative class). From historical experience, manual inspection correctly identifies 85% of loan defaulters in any given batch of only defaulter customers.
The top brass at ML, Dr. Milo, has embarked on a journey in business analytics. Hence, he has decided to replace the manual inspection with an Automatic Defaulter Detection System (ADDS). This ADDS runs a trained logistic model in the background which classifies an applicant as “Defaulter” or “Non-Defaulter” based on the scores for “Earnings” and “Tenure”. To test the ADDS, a sample of 200 applications are taken. The sample is imbalanced and only 30% of the sample applicants were non-defaulters. The sample applications are passed through the ADDS, and the system identifies 70% of the actual non-defaulters as defaulters and 10% of actual defaulters as non-defaulters.
Using this information, answer the given subquestions.

What is the specificity of the ADDS?
(Note: Enter the answer as a numeric percentage value rounded to two decimal places without the % symbol. For example, if your answer is “10.256 %”, enter it as “10.26”)

“Milo Loner (ML)” is a bank that gives out personal loans to customers. Currently, the process of document verification is done manually by verifying the scores from 2 variables “Earnings” and “Tenure”. The aim of inspection process is to identify customers who will default on a loan (considered as the negative class). From historical experience, manual inspection correctly identifies 85% of loan defaulters in any given batch of only defaulter customers.
The top brass at ML, Dr. Milo, has embarked on a journey in business analytics. Hence, he has decided to replace the manual inspection with an Automatic Defaulter Detection System (ADDS). This ADDS runs a trained logistic model in the background which classifies an applicant as “Defaulter” or “Non-Defaulter” based on the scores for “Earnings” and “Tenure”. To test the ADDS, a sample of 200 applications are taken. The sample is imbalanced and only 30% of the sample applicants were non-defaulters. The sample applications are passed through the ADDS, and the system identifies 70% of the actual non-defaulters as defaulters and 10% of actual defaulters as non-defaulters.
Using this information, answer the given subquestions.

What is the sensitivity of the ADDS?
(Note: Enter the answer as a numeric percentage value rounded to two decimal places without the % symbol. For example, if your answer is “10.256 %”, enter it as “10.26”)

“Milo Loner (ML)” is a bank that gives out personal loans to customers. Currently, the process of document verification is done manually by verifying the scores from 2 variables “Earnings” and “Tenure”. The aim of inspection process is to identify customers who will default on a loan (considered as the negative class). From historical experience, manual inspection correctly identifies 85% of loan defaulters in any given batch of only defaulter customers.
The top brass at ML, Dr. Milo, has embarked on a journey in business analytics. Hence, he has decided to replace the manual inspection with an Automatic Defaulter Detection System (ADDS). This ADDS runs a trained logistic model in the background which classifies an applicant as “Defaulter” or “Non-Defaulter” based on the scores for “Earnings” and “Tenure”. To test the ADDS, a sample of 200 applications are taken. The sample is imbalanced and only 30% of the sample applicants were non-defaulters. The sample applications are passed through the ADDS, and the system identifies 70% of the actual non-defaulters as defaulters and 10% of actual defaulters as non-defaulters.
Using this information, answer the given subquestions.

Should ADDS be implemented?

A kirana store owner has allocated a budget of Rs. 2,00,000 to buy fruits to sell in the store. The aim of the owner is to maximize the profit from selling fruits. The owner has decided to buy “Apples”, “Oranges”, “Mangoes”, “Banana” and “Guava”. The Apples are purchased at Rs. 40/piece, the Oranges at Rs. 12/piece, Mangos at Rs. 52/piece, Bananas at Rs. 2/piece and Guavas at Rs. 10/ piece. An apple is sold for Rs. 50/piece, Orange at Rs. 18/piece, Mango at Rs. 82/piece, Banana at Rs. 5/piece and Guava at Rs. 25/piece. Due to contractual restrictions, the owner cannot buy less than 100 Apples, 70 Oranges, 60 Mangoes, 200 Bananas and 100 Guavas. Additionally, the number of Apples purchased must be at least 30%more than total number of Bananas and Guavas purchased. The number of Bananas purchased must be greater than or equal to the number of Guavas purchased. The number of Oranges purchased must be equal to the number of Mangoes purchased. Finally, total number of fruit pieces that an owner can buy cannot be more than 8000. Given this information, answer the given subquestions.

How many decision variables are present in the standard form of the primal for the given problem?
(Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)

A kirana store owner has allocated a budget of Rs. 2,00,000 to buy fruits to sell in the store. The aim of the owner is to maximize the profit from selling fruits. The owner has decided to buy “Apples”, “Oranges”, “Mangoes”, “Banana” and “Guava”. The Apples are purchased at Rs. 40/piece, the Oranges at Rs. 12/piece, Mangos at Rs. 52/piece, Bananas at Rs. 2/piece and Guavas at Rs. 10/ piece. An apple is sold for Rs. 50/piece, Orange at Rs. 18/piece, Mango at Rs. 82/piece, Banana at Rs. 5/piece and Guava at Rs. 25/piece. Due to contractual restrictions, the owner cannot buy less than 100 Apples, 70 Oranges, 60 Mangoes, 200 Bananas and 100 Guavas. Additionally, the number of Apples purchased must be at least 30%more than total number of Bananas and Guavas purchased. The number of Bananas purchased must be greater than or equal to the number of Guavas purchased. The number of Oranges purchased must be equal to the number of Mangoes purchased. Finally, total number of fruit pieces that an owner can buy cannot be more than 8000. Given this information, answer the given subquestions.

Based on the standard form of the primal, how many decision variables will be present in the dual formulation?
(Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)

A kirana store owner has allocated a budget of Rs. 2,00,000 to buy fruits to sell in the store. The aim of the owner is to maximize the profit from selling fruits. The owner has decided to buy “Apples”, “Oranges”, “Mangoes”, “Banana” and “Guava”. The Apples are purchased at Rs. 40/piece, the Oranges at Rs. 12/piece, Mangos at Rs. 52/piece, Bananas at Rs. 2/piece and Guavas at Rs. 10/ piece. An apple is sold for Rs. 50/piece, Orange at Rs. 18/piece, Mango at Rs. 82/piece, Banana at Rs. 5/piece and Guava at Rs. 25/piece. Due to contractual restrictions, the owner cannot buy less than 100 Apples, 70 Oranges, 60 Mangoes, 200 Bananas and 100 Guavas. Additionally, the number of Apples purchased must be at least 30%more than total number of Bananas and Guavas purchased. The number of Bananas purchased must be greater than or equal to the number of Guavas purchased. The number of Oranges purchased must be equal to the number of Mangoes purchased. Finally, total number of fruit pieces that an owner can buy cannot be more than 8000. Given this information, answer the given subquestions.

Based on the standard form of the primal for the given problem, which of the following is/ are “RHS” values for the constraints in the Dual?

A kirana store owner has allocated a budget of Rs. 2,00,000 to buy fruits to sell in the store. The aim of the owner is to maximize the profit from selling fruits. The owner has decided to buy “Apples”, “Oranges”, “Mangoes”, “Banana” and “Guava”. The Apples are purchased at Rs. 40/piece, the Oranges at Rs. 12/piece, Mangos at Rs. 52/piece, Bananas at Rs. 2/piece and Guavas at Rs. 10/ piece. An apple is sold for Rs. 50/piece, Orange at Rs. 18/piece, Mango at Rs. 82/piece, Banana at Rs. 5/piece and Guava at Rs. 25/piece. Due to contractual restrictions, the owner cannot buy less than 100 Apples, 70 Oranges, 60 Mangoes, 200 Bananas and 100 Guavas. Additionally, the number of Apples purchased must be at least 30%more than total number of Bananas and Guavas purchased. The number of Bananas purchased must be greater than or equal to the number of Guavas purchased. The number of Oranges purchased must be equal to the number of Mangoes purchased. Finally, total number of fruit pieces that an owner can buy cannot be more than 8000. Given this information, answer the given subquestions.

Say the owner purchases 700 Apples, 800 Bananas, 500 Oranges, 500 Mangoes and 600 Guavas. Then how many constraints in the standard form of the primal will be binding?
(Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)

A kirana store owner has allocated a budget of Rs. 2,00,000 to buy fruits to sell in the store. The aim of the owner is to maximize the profit from selling fruits. The owner has decided to buy “Apples”, “Oranges”, “Mangoes”, “Banana” and “Guava”. The Apples are purchased at Rs. 40/piece, the Oranges at Rs. 12/piece, Mangos at Rs. 52/piece, Bananas at Rs. 2/piece and Guavas at Rs. 10/ piece. An apple is sold for Rs. 50/piece, Orange at Rs. 18/piece, Mango at Rs. 82/piece, Banana at Rs. 5/piece and Guava at Rs. 25/piece. Due to contractual restrictions, the owner cannot buy less than 100 Apples, 70 Oranges, 60 Mangoes, 200 Bananas and 100 Guavas. Additionally, the number of Apples purchased must be at least 30%more than total number of Bananas and Guavas purchased. The number of Bananas purchased must be greater than or equal to the number of Guavas purchased. The number of Oranges purchased must be equal to the number of Mangoes purchased. Finally, total number of fruit pieces that an owner can buy cannot be more than 8000. Given this information, answer the given subquestions.

Say the owner purchases 700 Apples, 800 Bananas, 500 Oranges, 500 Mangoes and 600 Guavas. Then what is the value of the objective function?
(Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)

You perform a Chi-square Test of Independence on a contingency table with 6 rows and 7 columns. The value of the computed test statistic is 30.24. Given this information and the Figure-1 below. Answer the given subquestions.

At a 5% confidence level, what is the value of the tabulated test statistic?
(Note: If your answer is in decimal, enter it rounded to two decimal places. For example, if your answer is “10.256”, enter it as “10.26”)

You perform a Chi-square Test of Independence on a contingency table with 6 rows and 7 columns. The value of the computed test statistic is 30.24. Given this information and the Figure-1 below. Answer the given subquestions.

Based on Figure-1, up to what (maximum) level of significance will the null hypothesis be rejected?
(Note: Enter the answer as a numeric percentage value rounded to two decimal places without the % symbol. For example, if your answer is “10.256 %”, enter it as “10.26”)

Which of the following are applications of logistic regression (choose all that may be applicable)?

Say a demand response curve is modelled as a constant elasticity curve. If Q1 is 4400 units, Q2 is 2500 units, P1 is Rs. 50 and P2 is Rs. 250, Then answer the given subquestions.

What is the elasticity of the curve?
(Note: If your answer is in decimal, enter it rounded to two decimal places. For example, if your answer is “10.256”, enter it as “10.26”)

Say a demand response curve is modelled as a constant elasticity curve. If Q1 is 4400 units, Q2 is 2500 units, P1 is Rs. 50 and P2 is Rs. 250, Then answer the given subquestions.

What is the value of the “constant” in the non-linear demand response curve function? (Note: If your answer is in decimal, enter it rounded to two decimal places. For example, if your answer is “10.256”, enter it as “10.26”)