Question

The following data comprising the number of customers (in hundred) and monthly sales (in thousand Rupees): 

Number of Customers (in
hundred)
4 6 6 8 10 14 18 20 22 26 28 30
Monthly Sales
(in thousand Rs)
1.8 3.5 5.8 7.8 8.7 9.8 10.7 11.5 12.9 13.6 14.2 15

 Calculate the residuals and determine the standardised residuals for the model Y = 2.6185 + 0.4369 X 

14 Feb 2023
Answer :
Word Count : 277

We can calculate the predicted values for the monthly sales using the given linear regression equation:

Y = 2.6185 + 0.4369X

Where Y is the monthly sales and X is the number of customers (in hundred).

Using this equation, we get the following predicted values:

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Predicted Y: 3.7986
Factory Godowns Stock
Available
1 2 3 4 5 6
A 7 5 7 7 5 3 60
B 9 11 6 11 - 5 20
C 11 10 6 2 2 8 90
D 9 10 9 6 9 12 50
Demand 60 20 40 20 40 40  

A Statistician collected the data of 78 values with two independent variable X1 and X2, and considered the four models: (i) Y = B0 + e;

(ii) Y = B0 + B1X1 + e;

(iii) Y = B0 + BX1 + e and

(iv) Y = B0 + B1 X1 + B2 X2 + e.

The results obtained are: σ2=0.91, SS(B0) = 652.42, SS(B0,B1) = 679.34, SS(B0,B2) = 654.00,SS(B0,B1,B2) = 687.79 . Find the additional contribution of (i) X2 over X1 and (ii) X1 over X2. Test whether their inclusion in the model is justified.

The following data comprising the number of customers (in hundred) and monthly sales (in thousand Rupees): 

Number of Customers (in
hundred)
4 6 6 8 10 14 18 20 22 26 28 30
Monthly Sales
(in thousand Rs)
1.8 3.5 5.8 7.8 8.7 9.8 10.7 11.5 12.9 13.6 14.2 15

State whether the following statements are True or False and also give the reason in support of your answer.
a) The Set $ ={(x, y) : 0 ≤ y ≤ 5 when 0 ≤ x≤ 2 and 3≤ y≤ 5 when 2≤ x ≤ 7 } is not a convex set.
b) If 10 is added to each of the entries of the cost matrix of a 3 x 3 assignment problem, then the total cost of an optimal assignment for the changed cost matrix will increase by 10.
c) The solution to a transportation problem with m-rows (supplies) and n-columns (destinations) is feasible if number of positive allocations is m + n.
d) The Value di ≥ 3 indicates an outlying observation in regression analysis.
e) Variations which occur due to natural forces and operate in a regular and periodic manner over a span of less than or equal to one year are termed as cyclic variations

A department head has four subordinates, and four tasks to be performed. The subordinates differ in efficiency, and the tasks differ in their intrinsic difficulty. His estimate, of the time each man would take to perform each task, is given in the table below:

Tasks Subordinates
E F G H
A 18 26 17 11
B 13 28 14 26
C 38 19 18 15
D 19 26 24 10

Use graphical method to minimise the time added to process the following jobs on the machines shown: 

Job 1: Sequence A B C D E
Time 3 4 2 6 2
Job 2: Sequence B C A D E
Time 5 4 3 2 6

Calculate seasonal indices by the ratio to moving average method from the following data:

Year
Quarter
2001 2002 2003 2004
Q1 750 860 900 1000
Q2 600 650 720 780
Q3 540 630 660 720
Q4 590 800 850 930
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