A statistician collected data of 78 values with two independent variable X1 and X2 . The four models considered are:
(a) Y = B0 + e, (b) Y = B0 + B1X1 (c) Y = B0 + B1X1 + B2X2 + e and (d) Y = B0 + B2X2 + e. The results are SS(B0) = 6524. 2, SS(B0,B1) = 6793.4, SS(B0,B2) = 6540.0,SS(B0,B1,B2) = 6877.9 and Find additional contribution of (i) X2 overX1 and (ii) X1 overX2 . Test whether their inclusion in the model is justified.
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The demand (in thousands of units) of refrigerators manufactured by a company are summarised in the following table:
| Year | Quarter | |||
| I | II | III | IV | |
| 2011 2012 2013 2014 | 124 104 80 116 | 120 128 152 156 | 176 148 168 184 | 140 132 156 180 |
A department has five employees with five jobs to be performed. The time (in hours) each man will take to perform each job is given in the effectiveness matrix:
| Employees | |||||
| Jobs | I | II | III | IV | V |
| A B C D E | 10 3 10 7 7 | 5 9 7 11 9 | 13 18 2 9 10 | 15 13 2 7 4 | 16 6 2 12 12 |
A statistician collected data of 78 values with two independent variable X1 and X2 . The four models considered are:
(a) Y = B0 + e, (b) Y = B0 + B1X1 (c) Y = B0 + B1X1 + B2X2 + e and (d) Y = B0 + B2X2 + e. The results are SS(B0) = 6524. 2, SS(B0,B1) = 6793.4, SS(B0,B2) = 6540.0,SS(B0,B1,B2) = 6877.9 and Find additional contribution of (i) X2 overX1 and (ii) X1 overX2 . Test whether their inclusion in the model is justified.
Arrivals at telephone booth are considered to be Poisson with an average time of 10 minutes between are arrival and the next. The length of phone call is assumed to be distributed exponentially with mean 3 minutes.
i) What is the probability that a person arriving at the booth will have to wait?
ii) The telephone department will install a second booth when convinced that an arrival would expect waiting for at least 3 minutes for phone call. By how much should the flow of arrivals increases in order to justify a second booth?
iii) What is the average length of the queen that forms from time to time?
iv) What is the probability that it will take him or her more than 10 minutes altogether to wait for the phone and complete his or her call?
The annual sales revenue (in lakhs of Rs) of a product as a function of sales force (number of salesmen) and annual adverting expenditure (in Thousands of Rs) for the past 10 years are summarised in following table:
| Annual Sales Revenue Y(in Lakhs) | Sales Force X1 (in Number) | Annual Advertising Expenditure X2 (in Thousand) |
| 100
115
125
135
105
145
110
120
135
175 | 40
65
40
90
115
80
50
60
70
100 | 140
115
190
80
100
140
115
150
130
160 |
For the following Auto regressive model
Xt = 0.7X t -1 - 0.4 Xt -2 + a t
i) Verify whether the series is Stationary
ii) Obtain pk : k = 1, 2 ,3, 4 and 5
iii) Plot the Correlogram.
A private company has two bottling plants located in city I and City II. Each plant produces three cold drinks Drink A, Drink B and Drink C. The number of bottles produced per day are as follows.
| Drink | Plant at | |
| City I | City II | |
| Drink A | 1,500 | 1,500 |
| Drink B | 3,000 | 1,000 |
| Drink C | 2,000 | 5,000 |