Business Analytics Quiz 2: 4 August 2024 (May 2024 term)

Milo’s Evaluation (ME) is a loan default prediction company that uses manual workforce to suggest possible defaulters. Dr. Milo, the Chief Data Officer of ME, has decided to replace the manual workforce with a cutting-edge Logistic Regression Model that takes “Age” and “Income” as parameters to predict defaulters. The model is configured such that a “Defaulter” is categorised as the positive class. The final model had the parameters as specified in Table-1 below. To test the model, the data in Table-2 is used as test data. Given this information, answer the given subquestions.

Table-1

Table-2

At a threshold of 0.8, how many “True Positives” is the model predicting?

Milo’s Evaluation (ME) is a loan default prediction company that uses manual workforce to suggest possible defaulters. Dr. Milo, the Chief Data Officer of ME, has decided to replace the manual workforce with a cutting-edge Logistic Regression Model that takes “Age” and “Income” as parameters to predict defaulters. The model is configured such that a “Defaulter” is categorised as the positive class. The final model had the parameters as specified in Table-1 below. To test the model, the data in Table-2 is used as test data. Given this information, answer the given subquestions.

Table-1

Table-2

At a threshold of 0.8, how many “True Negatives” is the model predicting?

Milo’s Evaluation (ME) is a loan default prediction company that uses manual workforce to suggest possible defaulters. Dr. Milo, the Chief Data Officer of ME, has decided to replace the manual workforce with a cutting-edge Logistic Regression Model that takes “Age” and “Income” as parameters to predict defaulters. The model is configured such that a “Defaulter” is categorised as the positive class. The final model had the parameters as specified in Table-1 below. To test the model, the data in Table-2 is used as test data. Given this information, answer the given subquestions.

Table-1

Table-2

At a threshold of 0.8, how many “False Positives” is the model predicting?

Milo’s Evaluation (ME) is a loan default prediction company that uses manual workforce to suggest possible defaulters. Dr. Milo, the Chief Data Officer of ME, has decided to replace the manual workforce with a cutting-edge Logistic Regression Model that takes “Age” and “Income” as parameters to predict defaulters. The model is configured such that a “Defaulter” is categorised as the positive class. The final model had the parameters as specified in Table-1 below. To test the model, the data in Table-2 is used as test data. Given this information, answer the given subquestions.

Table-1

Table-2

At a threshold of 0.8, how many “False Negatives” is the model predicting?

Milo’s Evaluation (ME) is a loan default prediction company that uses manual workforce to suggest possible defaulters. Dr. Milo, the Chief Data Officer of ME, has decided to replace the manual workforce with a cutting-edge Logistic Regression Model that takes “Age” and “Income” as parameters to predict defaulters. The model is configured such that a “Defaulter” is categorised as the positive class. The final model had the parameters as specified in Table-1 below. To test the model, the data in Table-2 is used as test data. Given this information, answer the given subquestions.

Table-1

Table-2

At a threshold of 0.5, what is the ACCURACY of the model? (Note: Enter the answer in “%” rounded to two decimal places without the “%” symbol. For example, if the answer is “1.234%”, then enter it as “1.23”)

Milo’s Evaluation (ME) is a loan default prediction company that uses manual workforce to suggest possible defaulters. Dr. Milo, the Chief Data Officer of ME, has decided to replace the manual workforce with a cutting-edge Logistic Regression Model that takes “Age” and “Income” as parameters to predict defaulters. The model is configured such that a “Defaulter” is categorised as the positive class. The final model had the parameters as specified in Table-1 below. To test the model, the data in Table-2 is used as test data. Given this information, answer the given subquestions.

Table-1

Table-2

At a threshold of 0.5, what is the PRECISION of the model for predicting the Negative Class? (Note: Enter the answer in “%” rounded to two decimal places without the “%” symbol. For example, if the answer is “1.234%”, then enter it as “1.23”)

Milo’s Evaluation (ME) is a loan default prediction company that uses manual workforce to suggest possible defaulters. Dr. Milo, the Chief Data Officer of ME, has decided to replace the manual workforce with a cutting-edge Logistic Regression Model that takes “Age” and “Income” as parameters to predict defaulters. The model is configured such that a “Defaulter” is categorised as the positive class. The final model had the parameters as specified in Table-1 below. To test the model, the data in Table-2 is used as test data. Given this information, answer the given subquestions.

Table-1

Table-2

At a threshold of 0.5, what is the RECALL of the model for predicting the Positive Class? (Note: Enter the answer in “%” rounded to two decimal places without the “%” symbol. For example, if the answer is “1.234%”, then enter it as “1.23”)

Milo’s Evaluation (ME) is a loan default prediction company that uses manual workforce to suggest possible defaulters. Dr. Milo, the Chief Data Officer of ME, has decided to replace the manual workforce with a cutting-edge Logistic Regression Model that takes “Age” and “Income” as parameters to predict defaulters. The model is configured such that a “Defaulter” is categorised as the positive class. The final model had the parameters as specified in Table-1 below. To test the model, the data in Table-2 is used as test data. Given this information, answer the given subquestions.

Table-1

Table-2

At a threshold of 0.5, what is the SENSITIVITY of the model? (Note: Enter the answer in “%” rounded to two decimal places without the “%” symbol. For example, if the answer is “1.234%”, then enter it as “1.23”)

A demand response curve has a constant elasticity of +0.4. If the price of the product is 100 and the corresponding demand is 200, then answer the given subquestions.

What is the intercept for the curve? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)

A demand response curve has a constant elasticity of +0.4. If the price of the product is 100 and the corresponding demand is 200, then answer the given subquestions.

What should be the price to achieve a demand of 300? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)

The demand of a product is estimated to follow the relationship: D(p) = 1444 – 3(p^2). Here, “p” is the selling price for the product. The product is made at Rs. 50 per unit. Given this information, answer the given subquestions.

If you intend to maximize the revenue, then what is optimal value for “p”? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)

The demand of a product is estimated to follow the relationship: D(p) = 1444 – 3(p^2). Here, “p” is the selling price for the product. The product is made at Rs. 50 per unit. Given this information, answer the given subquestions.

If you intend to maximize the profits, then what is optimal value for “p”? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)

“Fake Money (FM)” is an investment consulting firm.
Dr. Milo has approached FM with Rs. 1,00,000 for guidance on investment opportunities. Dr. Milo wants to invest the entire Rs. 1,00,000. FM’s top financial analyst recommends that all new investments be made in oil industry, steel industry or government bonds. Specifically, the analyst identified five investment opportunities and projected their annual rates of returns (which are specified in Table-1). Dr. Milo, is a guy who likes to distribute his investments. Hence, he has specified the following requirements to the analyst
1. Neither industry (oil or steel) should receive more than Rs. 50,000
2. Government bonds should be at least 25% of the steel industry investments
3. The investments in Bongu Oil, the high-return but high-risk investment, cannot be more than 60% of total oil industry investment

Given this information, answer the subquestions

How many decision variable(s) is/are present in the standard form of the primal?

“Fake Money (FM)” is an investment consulting firm.
Dr. Milo has approached FM with Rs. 1,00,000 for guidance on investment opportunities. Dr. Milo wants to invest the entire Rs. 1,00,000. FM’s top financial analyst recommends that all new investments be made in oil industry, steel industry or government bonds. Specifically, the analyst identified five investment opportunities and projected their annual rates of returns (which are specified in Table-1). Dr. Milo, is a guy who likes to distribute his investments. Hence, he has specified the following requirements to the analyst
1. Neither industry (oil or steel) should receive more than Rs. 50,000
2. Government bonds should be at least 25% of the steel industry investments
3. The investments in Bongu Oil, the high-return but high-risk investment, cannot be more than 60% of total oil industry investment

Given this information, answer the subquestions

How many constraints (excluding the non-negativity constraints) is/are present in the standard form of the primal?

“Fake Money (FM)” is an investment consulting firm.
Dr. Milo has approached FM with Rs. 1,00,000 for guidance on investment opportunities. Dr. Milo wants to invest the entire Rs. 1,00,000. FM’s top financial analyst recommends that all new investments be made in oil industry, steel industry or government bonds. Specifically, the analyst identified five investment opportunities and projected their annual rates of returns (which are specified in Table-1). Dr. Milo, is a guy who likes to distribute his investments. Hence, he has specified the following requirements to the analyst
1. Neither industry (oil or steel) should receive more than Rs. 50,000
2. Government bonds should be at least 25% of the steel industry investments
3. The investments in Bongu Oil, the high-return but high-risk investment, cannot be more than 60% of total oil industry investment

Given this information, answer the subquestions

How many constraints (excluding the non-negativity constraints) are present in the dual (which is based on the standard form of the primal)?

“Fake Money (FM)” is an investment consulting firm.
Dr. Milo has approached FM with Rs. 1,00,000 for guidance on investment opportunities. Dr. Milo wants to invest the entire Rs. 1,00,000. FM’s top financial analyst recommends that all new investments be made in oil industry, steel industry or government bonds. Specifically, the analyst identified five investment opportunities and projected their annual rates of returns (which are specified in Table-1). Dr. Milo, is a guy who likes to distribute his investments. Hence, he has specified the following requirements to the analyst
1. Neither industry (oil or steel) should receive more than Rs. 50,000
2. Government bonds should be at least 25% of the steel industry investments
3. The investments in Bongu Oil, the high-return but high-risk investment, cannot be more than 60% of total oil industry investment

Given this information, answer the subquestions

If FM has suggested the below distribution of investments, then how much money (total money) is projected to be in hand at the end of the first year? (Note: Enter the answer in “Rs.” rounded to two decimal places without the “Rs.” symbol. For example, if the answer is “Rs. 1.234”, then enter it as “1.23”)

“Fake Money (FM)” is an investment consulting firm.
Dr. Milo has approached FM with Rs. 1,00,000 for guidance on investment opportunities. Dr. Milo wants to invest the entire Rs. 1,00,000. FM’s top financial analyst recommends that all new investments be made in oil industry, steel industry or government bonds. Specifically, the analyst identified five investment opportunities and projected their annual rates of returns (which are specified in Table-1). Dr. Milo, is a guy who likes to distribute his investments. Hence, he has specified the following requirements to the analyst
1. Neither industry (oil or steel) should receive more than Rs. 50,000
2. Government bonds should be at least 25% of the steel industry investments
3. The investments in Bongu Oil, the high-return but high-risk investment, cannot be more than 60% of total oil industry investment

Given this information, answer the subquestions

If FM has suggested the below distribution of investments, then how many decision variables in the dual will have a non-zero value?

A multiple linear regression model, as specified below is fit on a data set with 50 data points.

Then answer the given subquestions

How many degrees of freedom are present for the “Residuals” in the ANOVA Table?

A multiple linear regression model, as specified below is fit on a data set with 50 data points.

Then answer the given subquestions

How many degrees of freedom are present for the “Regression” in the ANOVA Table?

A multiple linear regression model, as specified below is fit on a data set with 50 data points.

Then answer the given subquestions

How many total degrees of freedom are present for the fitted model in the ANOVA Table?

A multiple linear regression model, as specified below is fit on a data set with 50 data points.

Then answer the given subquestions

If the SSE and SST for the model are 900 and 1400 respectively, then what is the value for the model’s F-statistic? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)

A multiple linear regression model, as specified below is fit on a data set with 50 data points.

Then answer the given subquestions

If the SSE and SST for the model are 900 and 1400 respectively, then what is the Adjusted R-square value for model? (Note: Enter the answer in “%” rounded to two decimal places without the “%” symbol. For example, if the answer is “1.234%”, then enter it as “1.23”)