Decision Science- NMIMS Latest solved assignments

 

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Decision Science

April 2021 Examination

Q1. Considering Y as a dependent variable, a regression model is applied with three independent variables X1 X2 and X3. The results of the regression analysis are shown below:

 

 

1. Define R and R Square.

Ans 1.

 

R= Correlation coefficient

R is a statistical measure of

 

 

2. What is the significance of F test?

Ans 2.

 

The significance F gives the probability that the model is wrong.

 

Statistically, th

 

 

3. Which variable has the highest impact on Y.?

Ans 3.

X4 variable has the highest impact on y.

Because t

 

 

4. Write the regression equation.

 

Ans :

 

The regression equation is,

 

Regression analysis is a statistical technique which can evaluate the hypothesis that one or more other variables

 

 

 

5. Calculate Y if X1= 10, X2 =20 and X3 =5

 

Ans :

 

X1= 10, x2=20, x3=5.

 

 

 

Q2. The monthly sales (number of Cars sold) are recorded of a car dealer. Following ungrouped is available

 

52 33 70 95 57 61

57 64 54 94 38 61

50 39 94 63 59 31

68 88 93 48 82 82

74 70 92 76 98 91

32 33 31 75 54 48

36 64 63 66 92 98

36 54 71 86 84 55

91 34 64 67 89 78

97 92 53 56 68 55

93 42 51 77 36 93

44 66 63 33 68 79

83 53 86 76 35 40

55 41 36 39 42 96

60 53 38 51 95 56

48 69 49 33 95 37

83 62 96 34 85 32

39 59 77 62 35 34

54 89 36 45 83 34

39 61 88 86 55 33

a. Prepare the frequency distribution table showing the class interval (less than 10, 11 to 20, and so on), frequency of each class interval and cumulative frequency.

b. Calculate the mean, median, mode and quartiles of grouped data.

c. Calculate the standard deviation, variance and range

d. Make the following diagrams: Histogram, Frequency Polygon, Ogive (10 Marks)

Ans 2.

 

Q3a. It is estimated that 50% of emails are spam emails. Some software has been applied to filter these spam emails before they reach your inbox. A certain brand of software claims that it can detect 99% of spam emails, and the probability for a false positive (a non-spam email detected as spam) is 5%. Now if an email is detected as spam, then what is the probability that it is in fact a non-spam email? (5 Marks)

Ans 3a.

This question is based on Bayes’ probability equation.

Bayes’ Theorem is used to find

 

Q3b. The time taken to assemble a car in a certain plant is a random variable having a normal distribution of 20 hours and a standard deviation of 2 hours. What is the probability that a car can be assembled at this plant in a period of time?

a) Less than 19.5 hours?

Ans 3b.

Ans a.

 

 

 

 

b) Between 20 and 22 hours? (5 Marks)

Ans b.

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