NMIMS Global Access
School for Continuing Education (NGA-SCE)
Course: Decision Science

Internal Assignment Applicable for April 2021 Examination

1. 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:

Model R R Square Adjusted R Square
1 .969a

.939 .930

ANOVAa

Model Sum of Squares df Mean Square F Sig.

1
Regression 1123.258 3 374.419 97.893 .000b
Residual 72.671 19 3.825
Total 1195.929 22
a. Dependent Variable: Y
b. Predictors: (Constant), X5, X3, X4

Coefficientsa

Model Unstandardized Coefficients Standardized
Coefficients

t Sig.

B Std. Error Beta

1
(Constant) 35.681 3.399 10.496 .000
X3 -.654 .158 -.986 -4.151 .001
X4 .233 .054 1.111 4.275 .000
X5 .115 .024 .806 4.749 .000
a. Dependent Variable: Y

2. What is the significance of F test.
3. Which variable has the highest impact on Y.
4. Write the regression equation.
5. Calculate Y if X1= 10, X2 =20 and X3 =5
(10 Marks)

2. The monthly sales (number of Cars sold) is 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)

3.a. 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)

3.b. 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?
b) between 20 and 22 hours?