Business Analytics End Term: 3 September 2023, Set QPD1-S2 (May 2023 term)

In an ideal scenario, if a distribution has “Negative Skewness” then,

A company produces a car in two locations “A” and “B” using the same manufacturing process. A total of 20 cars in each location were taken and the number of defects in each car was computed. It has been established that the maximum number of defects per car is 5. Given this data in Table- 1, answer the given sub-questions.

Table- 1

If the focus is on seeing the distribution of defects (presented in Table-1) across the two locations, then which among the following graphs will be best suited? (Note: While choosing an answer to this question, please do not worry about colour reproduction or other aesthetics. Make a choice only based on the concepts of visualization theory)

A company produces a car in two locations “A” and “B” using the same manufacturing process. A total of 20 cars in each location were taken and the number of defects in each car was computed. It has been established that the maximum number of defects per car is 5. Given this data in Table- 1, answer the given sub-questions.

Table- 1

If the aim is to determine if the defect occurrence is independent of location, then how many cars would you expect to have “4” defects in Location A? (Round your answer to two decimal places. Eg: If your answer is 10.256, then round it to 10.26)

A company produces a car in two locations “A” and “B” using the same manufacturing process. A total of 20 cars in each location were taken and the number of defects in each car was computed. It has been established that the maximum number of defects per car is 5. Given this data in Table- 1, answer the given sub-questions.

Table- 1

If the aim is to determine if the defect occurrence is independent of location, then how many cars would you expect to have “1” defect in Location B? (Round your answer to two decimal places. Eg: If your answer is 10.256, then round it to 10.26)

A company produces a car in two locations “A” and “B” using the same manufacturing process. A total of 20 cars in each location were taken and the number of defects in each car was computed. It has been established that the maximum number of defects per car is 5. Given this data in Table- 1, answer the given sub-questions.

Table- 1

If the aim is to find if the number of defects is independent of location, then what is the value for the test statistic? (Round your answer to two decimal places. Eg: If your answer is 10.256, then round it to 10.26)

A company produces a car in two locations “A” and “B” using the same manufacturing process. A total of 20 cars in each location were taken and the number of defects in each car was computed. It has been established that the maximum number of defects per car is 5. Given this data in Table- 1, answer the given sub-questions.

Table- 1

The general belief is that the total number of defects across all different locations follows a Poisson distribution (whose PMF is given by the formula $\frac{e^{-\lambda} * \lambda^x}{x!}$).

To validate this belief, what is the value of the computed test statistic?

(Round your answer to two decimal places. Eg: If your answer is 10.256, then round it to 10.26)

A company produces a car in two locations “A” and “B” using the same manufacturing process. A total of 20 cars in each location were taken and the number of defects in each car was computed. It has been established that the maximum number of defects per car is 5. Given this data in Table- 1, answer the given sub-questions.

Table- 1

For the hypothesis test in the previous question, what (count) is the degrees of freedom?

Chef Jeff is curious to see about his LPG gas connection. He is of the opinion that gas consumption depends on the type of food (“baked items” or “fried items”) he prepares. Hence, over the past month, he has monitored his gas consumption for various items he has prepared (please do not worry about how the data is generated, it is not in the scope of the question). Using this data, Chef Jeff has built several regression models (Model-1, Model-2 and Model-3) which are specified below. He is happy with a 95% Confidence level. Given this information, answer the given subquestions. ( Note: For all the sub-questions, round your answer to two decimal places. Eg: If your answer is 10.256, then round it to 10.26)

Model-1 Consumption Vs Baked Items

ANOVA

Model-1

Model-2 Consumption vs Fried Items

ANOVA

Model-2

Model-3 Fried Items vs Baked Items

ANOVA

Model-3

What is the direct effect of cooking “baked items” on gas consumption?

Chef Jeff is curious to see about his LPG gas connection. He is of the opinion that gas consumption depends on the type of food (“baked items” or “fried items”) he prepares. Hence, over the past month, he has monitored his gas consumption for various items he has prepared (please do not worry about how the data is generated, it is not in the scope of the question). Using this data, Chef Jeff has built several regression models (Model-1, Model-2 and Model-3) which are specified below. He is happy with a 95% Confidence level. Given this information, answer the given subquestions. ( Note: For all the sub-questions, round your answer to two decimal places. Eg: If your answer is 10.256, then round it to 10.26)

Model-1 Consumption Vs Baked Items

ANOVA

Model-1

Model-2 Consumption vs Fried Items

ANOVA

Model-2

Model-3 Fried Items vs Baked Items

ANOVA

Model-3

Is there multi-collinearity present in the data set?

Chef Jeff is curious to see about his LPG gas connection. He is of the opinion that gas consumption depends on the type of food (“baked items” or “fried items”) he prepares. Hence, over the past month, he has monitored his gas consumption for various items he has prepared (please do not worry about how the data is generated, it is not in the scope of the question). Using this data, Chef Jeff has built several regression models (Model-1, Model-2 and Model-3) which are specified below. He is happy with a 95% Confidence level. Given this information, answer the given subquestions. ( Note: For all the sub-questions, round your answer to two decimal places. Eg: If your answer is 10.256, then round it to 10.26)

Model-1 Consumption Vs Baked Items

ANOVA

Model-1

Model-2 Consumption vs Fried Items

ANOVA

Model-2

Model-3 Fried Items vs Baked Items

ANOVA

Model-3

What is the value of X1?

Chef Jeff is curious to see about his LPG gas connection. He is of the opinion that gas consumption depends on the type of food (“baked items” or “fried items”) he prepares. Hence, over the past month, he has monitored his gas consumption for various items he has prepared (please do not worry about how the data is generated, it is not in the scope of the question). Using this data, Chef Jeff has built several regression models (Model-1, Model-2 and Model-3) which are specified below. He is happy with a 95% Confidence level. Given this information, answer the given subquestions. ( Note: For all the sub-questions, round your answer to two decimal places. Eg: If your answer is 10.256, then round it to 10.26)

Model-1 Consumption Vs Baked Items

ANOVA

Model-1

Model-2 Consumption vs Fried Items

ANOVA

Model-2

Model-3 Fried Items vs Baked Items

ANOVA

Model-3

What is the value of X2?

Chef Jeff is curious to see about his LPG gas connection. He is of the opinion that gas consumption depends on the type of food (“baked items” or “fried items”) he prepares. Hence, over the past month, he has monitored his gas consumption for various items he has prepared (please do not worry about how the data is generated, it is not in the scope of the question). Using this data, Chef Jeff has built several regression models (Model-1, Model-2 and Model-3) which are specified below. He is happy with a 95% Confidence level. Given this information, answer the given subquestions. ( Note: For all the sub-questions, round your answer to two decimal places. Eg: If your answer is 10.256, then round it to 10.26)

Model-1 Consumption Vs Baked Items

ANOVA

Model-1

Model-2 Consumption vs Fried Items

ANOVA

Model-2

Model-3 Fried Items vs Baked Items

ANOVA

Model-3

What is the value of X3?

Chef Jeff is curious to see about his LPG gas connection. He is of the opinion that gas consumption depends on the type of food (“baked items” or “fried items”) he prepares. Hence, over the past month, he has monitored his gas consumption for various items he has prepared (please do not worry about how the data is generated, it is not in the scope of the question). Using this data, Chef Jeff has built several regression models (Model-1, Model-2 and Model-3) which are specified below. He is happy with a 95% Confidence level. Given this information, answer the given subquestions. ( Note: For all the sub-questions, round your answer to two decimal places. Eg: If your answer is 10.256, then round it to 10.26)

Model-1 Consumption Vs Baked Items

ANOVA

Model-1

Model-2 Consumption vs Fried Items

ANOVA

Model-2

Model-3 Fried Items vs Baked Items

ANOVA

Model-3

What is the value of X4?

Chef Jeff is curious to see about his LPG gas connection. He is of the opinion that gas consumption depends on the type of food (“baked items” or “fried items”) he prepares. Hence, over the past month, he has monitored his gas consumption for various items he has prepared (please do not worry about how the data is generated, it is not in the scope of the question). Using this data, Chef Jeff has built several regression models (Model-1, Model-2 and Model-3) which are specified below. He is happy with a 95% Confidence level. Given this information, answer the given subquestions. ( Note: For all the sub-questions, round your answer to two decimal places. Eg: If your answer is 10.256, then round it to 10.26)

Model-1 Consumption Vs Baked Items

ANOVA

Model-1

Model-2 Consumption vs Fried Items

ANOVA

Model-2

Model-3 Fried Items vs Baked Items

ANOVA

Model-3

Which regression model(s) is (are) significant (select all that is applicable)

The demand for cool drinks at different prices in the supermarket at IITM is specified in Figure-1. Given this data, if the demand is expected to follow a constant elasticity curve, then answer the given subquestions (Note: For all the sub-questions, round your answer to two decimal places.Eg: If your answer is 10.256, then round it to 10.26)

What is the elasticity of the demand-response curve?

The demand for cool drinks at different prices in the supermarket at IITM is specified in Figure-1. Given this data, if the demand is expected to follow a constant elasticity curve, then answer the given subquestions (Note: For all the sub-questions, round your answer to two decimal places.Eg: If your answer is 10.256, then round it to 10.26)

What is the maximum possible demand for cool drinks at IITM?

You are given the following primal formulation. The optimal solution to the formulated problem yields the value $X_1^* = 3$, $X_2^* =0$, $X_3^*=1$, $X_4^*=5$. Then answer the given sub-questions.

Minimize $z = 2X_1 + 4X_2+ 4X_3 - 3X_4$

Subject To

Constraint-1: $X_1+X_2+X_3 = 4$

Constraint-2: $X_1+4X_2+X_4 = 8$

Constraint-3: $X_1 + X_2 >= 3$

Constraint-4: $X_3 + X_4 <= 7$

Non-Negativity: $X_1$, $X_2$, $X_3$, $X_4 >=0$

How many decision variables are present in the dual formulation?

You are given the following primal formulation. The optimal solution to the formulated problem yields the value $X_1^* = 3$, $X_2^* =0$, $X_3^*=1$, $X_4^*=5$. Then answer the given sub-questions.

Minimize $z = 2X_1 + 4X_2+ 4X_3 - 3X_4$

Subject To

Constraint-1: $X_1+X_2+X_3 = 4$

Constraint-2: $X_1+4X_2+X_4 = 8$

Constraint-3: $X_1 + X_2 >= 3$

Constraint-4: $X_3 + X_4 <= 7$

Non-Negativity: $X_1$, $X_2$, $X_3$, $X_4 >=0$

How many decision variables in the optimal solution of the dual will have a value of “0”?

Organizations that do not find themselves on the Economic Frontier are called:

If the attribute values in the conjoint analysis is a continuous variable and the data is collected in a pairwise order, then what approach can be used: (select all that is applicable)

In the below diagram, the customer wants to decide between the products O1 & O2, and x denotes the coordinates of the ideal product. Which of the following are true?

Identify the most efficient Manufacturing unit from the graph given below. Assume the output of interest is profit and the input as manufacturing cost:

Identify the efficient business unit(s) from the graph given below:

How many dimensions of inputs/outputs be visualized in the graphical method:

Let us assume 5 DMUs in a DEA problem. Also, assume this as a two inputs and one output problem. Output of all DMUs are 5,00,000 and the reference units for DMU 1 are 2 and 5. The inputs of DMU 2 are (1,00,000 and 8). Similarly, the inputs of DMU 5 are (75,000 and 10). We are solving the problem for DMU 1, and dual variables for DMU 2 is 0.65 and DMU 5 is 0.35. Calculate the required level of input 1 for HCU 1.

Let us assume 5 DMUs in a DEA problem. Also, assume this as two inputs and one output problem. Output of all DMUs are 5,00,000 and the reference units for DMU 1 are the DMUs 2 and 5. The inputs of DMU 2 are (1,00,000 and 8). Similarly, the inputs of DMU 5 are (75,000 and 10). We are solving the problem for DMU 1, and dual variables for DMU 2 is 0.65 and DMU 5 is 0.35. Calculate the required level of input 2 for HCU 1.

In a conjoint problem with 4 products and 2 attributes, how many pair-wise preferences are possible?

Using the below confusion matrix answer the given subquestions.

How many “True Positives” is the model predicting?

Using the below confusion matrix answer the given subquestions.

How many “True Negatives” is the model predicting?

Using the below confusion matrix answer the given subquestions.

How many “False Positives” is the model predicting?

Using the below confusion matrix answer the given subquestions.

How many “False Negatives” is the model predicting?

Using the below confusion matrix answer the given subquestions.

What is the accuracy of the model? (Note: Give your answer in DECIMAL Values rounded to two digits. For example, if your answer is “0.256”, then enter it as “0.26”)

Using the below confusion matrix answer the given subquestions.

What is the precision of the model in predicting the “Negative class”? (Note: Give your answer in DECIMAL Values rounded to two digits. For example, if your answer is “0.256”, then enter it as “0.26”)

Using the below confusion matrix answer the given subquestions.

What is the recall of the model in predicting the “Positive class”? (Note: Give your answer in DECIMAL Values rounded to two digits. For example, if your answer is “0.256”, then enter it as “0.26”)