Business Analytics End Term: 30 April 2023, Set QPD1-S2 (January 2023 term)

In Regression, “Marginal” slope and “Partial” slope coincide if the explanatory variables are dependent.

The data on emissions from vehicular traffic for the first six months in 2023 and 2022 are provided in the Table below. If an analyst wants to develop a visualization that highlights “The months with the highest increase in emissions in 2023 as compared to 2022”, then which of the formulas would be apt to capture the required information for presentation

You are solving a regression problem with 8 explanatory variables. The data has 150 observations, and the R-square value was found to be 0.75. You are adding one more explanatory variable to the dataset, making a total of 9 variables. The adjusted R square value increases to 0.86. What does it signify?

How is Hypothetical Composite Unit computed in DEA for a DMU using graphical method?

How to identify the HCU of an inefficient DMU using Linear Programming Method?

The following is the Primal LP Formulation for a resource allocation problem. Given this, answer the subquestions

Objective: Maximize $(10Y_1 + 20Y_2 + 5Y_3 + 7Y_4 + 12Y_5 + 11Y_6)$

Constraint-1: $Y_1+Y_2+Y_3+Y_4+Y_5+Y_6 <= 200$

Constraint-2: $2Y_1+3Y_3 <= 50$

Constraint-3: $4Y_2+5Y_4+3Y_6 <= 70$

Constraint-4: $Y_1+ Y_3 <= 20$

Constraint-5: $Y_2+Y_4+Y_6 <= 70$

Constraint-6: $Y_1$, $Y_2$, $Y_3$, $Y_4$, $Y_5$, $Y_6$ are all non-negative

How many constraints will be present in the dual formulation?

The following is the Primal LP Formulation for a resource allocation problem. Given this, answer the subquestions

Objective: Maximize $(10Y_1 + 20Y_2 + 5Y_3 + 7Y_4 + 12Y_5 + 11Y_6)$

Constraint-1: $Y_1+Y_2+Y_3+Y_4+Y_5+Y_6 <= 200$

Constraint-2: $2Y_1+3Y_3 <= 50$

Constraint-3: $4Y_2+5Y_4+3Y_6 <= 70$

Constraint-4: $Y_1+ Y_3 <= 20$

Constraint-5: $Y_2+Y_4+Y_6 <= 70$

Constraint-6: $Y_1$, $Y_2$, $Y_3$, $Y_4$, $Y_5$, $Y_6$ are all non-negative

How many decision variables will be required to formulate the dual?

The following is the Primal LP Formulation for a resource allocation problem. Given this, answer the subquestions

Objective: Maximize $(10Y_1 + 20Y_2 + 5Y_3 + 7Y_4 + 12Y_5 + 11Y_6)$

Constraint-1: $Y_1+Y_2+Y_3+Y_4+Y_5+Y_6 <= 200$

Constraint-2: $2Y_1+3Y_3 <= 50$

Constraint-3: $4Y_2+5Y_4+3Y_6 <= 70$

Constraint-4: $Y_1+ Y_3 <= 20$

Constraint-5: $Y_2+Y_4+Y_6 <= 70$

Constraint-6: $Y_1$, $Y_2$, $Y_3$, $Y_4$, $Y_5$, $Y_6$ are all non-negative

What is the objective function “co-efficient” for the dual decision variable corresponding to the “Constraint-4” in the primal?

The following is the Primal LP Formulation for a resource allocation problem. Given this, answer the subquestions

Objective: Maximize $(10Y_1 + 20Y_2 + 5Y_3 + 7Y_4 + 12Y_5 + 11Y_6)$

Constraint-1: $Y_1+Y_2+Y_3+Y_4+Y_5+Y_6 <= 200$

Constraint-2: $2Y_1+3Y_3 <= 50$

Constraint-3: $4Y_2+5Y_4+3Y_6 <= 70$

Constraint-4: $Y_1+ Y_3 <= 20$

Constraint-5: $Y_2+Y_4+Y_6 <= 70$

Constraint-6: $Y_1$, $Y_2$, $Y_3$, $Y_4$, $Y_5$, $Y_6$ are all non-negative

Which of the following is/ are valid constraints/ objective function in the dual formulation for the provided primal formulation
{Note: Xi – represents the i^(th) decision variable in the dual formulation}

A logistic regression model is fit to predict if a student will pass the BA course (Y=1 pass, Y=0 fail). The results of the fitted model are given in the table below. Then answer the given subquestions.

Considering a threshold of 0.7, how many “True Positives” are present in the confusion matrix if the aim is to predict if a student will pass the course?
NOTE: Enter the answer as a numeric percentage value rounded to the nearest integer without the % symbol.

A logistic regression model is fit to predict if a student will pass the BA course (Y=1 pass, Y=0 fail). The results of the fitted model are given in the table below. Then answer the given subquestions.

Considering a threshold of 0.7, how many “False Positives” are present in the confusion matrix if the aim is to predict if a student will pass the course?
NOTE: Enter the answer as a numeric percentage value rounded to the nearest integer without the % symbol.

A logistic regression model is fit to predict if a student will pass the BA course (Y=1 pass, Y=0 fail). The results of the fitted model are given in the table below. Then answer the given subquestions.

Considering a threshold of 0.7, how many “False Negatives” are present in the confusion matrix if the aim is to predict if a student will pass the course?
NOTE: Enter the answer as a numeric percentage value rounded to the nearest integer without the % symbol.

A logistic regression model is fit to predict if a student will pass the BA course (Y=1 pass, Y=0 fail). The results of the fitted model are given in the table below. Then answer the given subquestions.

Considering a threshold of 0.7, how many “True Negatives” are present in the confusion matrix if the aim is to predict if a student will pass the course?
NOTE: Enter the answer as a numeric percentage value rounded to the nearest integer without the % symbol.

A logistic regression model is fit to predict if a student will pass the BA course (Y=1 pass, Y=0 fail). The results of the fitted model are given in the table below. Then answer the given subquestions.

What is the accuracy of the built logistic model for predicting if a student will fail the course if a threshold of 0.7 is taken?
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 logistic regression model is fit to predict if a student will pass the BA course (Y=1 pass, Y=0 fail). The results of the fitted model are given in the table below. Then answer the given subquestions.

What is the precision of the built logistic model for predicting if a student will pass the course if a threshold of 0.7 is taken?
NOTE: Enter the answer as a numeric percentage value rounded to the nearest integer without the % symbol.

A logistic regression model is fit to predict if a student will pass the BA course (Y=1 pass, Y=0 fail). The results of the fitted model are given in the table below. Then answer the given subquestions.

What is the recall of the built logistic model for predicting if a student will fail the course if a threshold of 0.7 is taken?
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”

You are given the sales volume of three brands, “A”, “B”, and “C” in 4 cities in the table below. Using this information, answer the given subquestions.

What is the expected frequency of “Chennai” people preferring “Brand-B”?
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 are given the sales volume of three brands, “A”, “B”, and “C” in 4 cities in the table below. Using this information, answer the given subquestions.

What is the expected frequency for “Delhi” people preferring “Brand-C”?
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 are given the sales volume of three brands, “A”, “B”, and “C” in 4 cities in the table below. Using this information, answer the given subquestions.

What is the value of the computed Chi-Square 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 are given the sales volume of three brands, “A”, “B”, and “C” in 4 cities in the table below. Using this information, answer the given subquestions.

What is the degrees of freedom for the chi-square test that you perform for this problem? NOTE: Enter your answer to the nearest integer.

You are given the sales volume of three brands, “A”, “B”, and “C” in 4 cities in the table below. Using this information, answer the given subquestions.

At the significance level 0.01, chi-squared tabular value is 16.18. What do you conclude?

When do you choose “charts” for representing data?

When performing the goodness of fit test by grouping the given observations into bins, the expected frequency represents the __ (choose all that are applicable)

If a constant elasticity curve models the demand response curve for the data given in the following table, then answer the given subquestions

What is the demand when the price is Rs.1?

If a constant elasticity curve models the demand response curve for the data given in the following table, then answer the given subquestions

What is the price elasticity for the demand response curve?

The relationship between Demand “D” and Selling Price “P” is given by the equation D(p) = 120 – 5*P. If the intention is to maximize the profit, then what is the optimal selling price if the item is going to be sold at Rs. 20 per unit?

There are 6 business units. There are two outputs and one input under consideration. You are solving the optimization problem for business unit 4 and find that the efficiency is 0.8. You find that the dual variables corresponding to the constraints of business units 3 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 3 and 5 are 0.3 and 0.5 respectively. You are given the following table where sales and number of leads are the two outputs. What is the sales in HCU 4?

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)

What is productive efficiency?

There are 7 business units and you are using the DEA to compare them. You solve the LP for business unit 4. You find from the constraint expression that business unit 2 has obtained an efficiency of 1 and business unit 7 has obtained an efficiency of 1 with the optimal weights of business unit 5. Which of the following statements is correct?