A researcher is interested in developing a linear model for the electricity consumption of a household having an AC (1.5 ton) so that she can predict the electricity consumption. For this purpose, she selects 25 houses and records the electricity consumption (in kWh), size of house (in square feet) and AC hours for one month during summers. The results obtained are:$
$
Build a regression model by selecting appropriate regressors in the model using the Stepwise Selection method.
______ _________ ________ ________ _______ _____ ______ ___ ___ ___ ______ __________.
_____ _____ ______ _________ _________ _________ ________ _____ __________ ______.
__________ ____ _____ ______ ____ ________.
___ ___ __________ ______ __________ _____ __________ ________.
__________ _____ ____ ___ ______ _______ _________ ____ ___ ________.
________ ________ ___ ________ _________ __________ ____ ________ __________ ____.
________ _____ _______ _________ _________ _____ __________ _______ _________ ___ ______.
_________ ____ _______ __________ ______ ______ ______ ____ ________.
________ _________ ________ _________ ________ ___ __________ __________ ___ _________ ___ ______.
____ __________ ________ ___ ________ _____ ______ ______.
________ ____ __________ ______ _______ ____ _____ ____ ______.
______ ___ _____ ________ ____ __________ _________ __________.
_____ __________ _________ ______ ____ _____ _______ _________ ____ _______ _________.
____ ________ ___ __________ _______ __________ _______ ________.
____ ____ ____ ______ ___ _________ _________ _________.
_______ ________ ___ ________ ________ ____ ___.
__________ _____ _________ ____ _____.
________ _________ ____ _____ ______ ___ _______ _________ ________ _________.
____ _________ __________ ___ __________ __________ _______.
_____ __________ _____ _________ ____ _________ ______ _____.
______ __________ _____ _________ _________ ________ ____.
__________ _____ _____ __________ ___ ______ ________ _______ _________.
___ _____ ___ ____ ___ ____ ___ __________ _______ _________ _____ _____.
__________ _______ _________ _________ ________ _______ _______ _____ ________ _____.
____ __________ ___ _________ ______ ________ ________ ___ _______ ___ ______.
______ ____ ___ _______ _____ ______ __________ __________ _________ ___ __________ __________.
________ ___ ___ ______ _______ _______.
__________ _______ _____ ___ _____ ______ ___ _______ ____ ___ ___.
____ _____ _____ __________ _________ ___ ________ ________ ____.
____ _________ _______ ___ __________ ____ ________ _____ __________ _______.
____ ____ ____ ______ __________ _____.
_________ _______ ____ _______ _________ _____.
__________ _______ __________ ________ _________ ____ __________ _____ ________ ________ ___ ______.
______ _____ ______ _________ _____.
________ ____ _______ ___ _________ ____ _______ ______ _______.
___ ________ _________ __________ ______ ___ __________ ___ ____ __________ ______.
____ ______ _________ ________ _____ ____.
- Solved Assignments
- Study Notes
- Guess Papers
- Question Papers
✓ Unlock up to 60% of the answer
✓ No payment required
A company has three production facilities S1, S2 and S3 with production capacity of 7, 9 and 18 units (in 100s) per week of a product, respectively. These units are to be shipped to four warehouses D1, D2, D3 and D4 with requirement of 5, 6, 7 and 14 units (in 100s) per week, respectively. The transportation costs (in Rs) per unit between factories to warehouses are given in the table below:
| $D_1$ | $D_2$ | $D_3$ | $D_4$ | Capacity | |
|---|---|---|---|---|---|
| $S_1$ | 19 | 30 | 50 | 10 | 7 |
| $S_2$ | 70 | 30 | 40 | 60 | 9 |
| $S_3$ | 40 | 8 | 70 | 20 | 18 |
| Demand | 5 | 8 | 7 | 14 | 34 |
A firm wants to know whether there is any linear relationship between the sales (X) and its yearly revenue (Y). The records for 10 years were examined and the following results were obtained:$
(a) Fit a regression line taking Y as the dependent variable and X as the independent variable.
(b) Test whether the sales have any effect on revenue at 5% level of significance.
(c) Comment on the goodness of fit of the regression line.
The following table represents the sales (in thousands) of mobile sets of a shop for 16 quarters over four years:
| Year | Quarter | |||
|---|---|---|---|---|
| Q_1 | Q_2 | Q_3 | Q_4 | |
| 2011 | 554 | 590 | 616 | 653 |
| 2012 | 472 | 501 | 521 | 552 |
| 2013 | 501 | 531 | 553 | 595 |
| 2014 | 403 | 448 | 460 | 480 |
In a railway marshalling yard, goods trains arrive at a rate of 36 trains per day. Assuming that the inter-arrival and service time distributions both follow exponential distribution with an average of 30 minutes, calculate the following:
(i) Traffic intensity
(ii) The mean queue length
(iii) Probability that the queue size exceeds
Use the penalty (Big M) method to solve the following LP problem:
Minimise
Subject to the constraints.
Seven successive observations on a stationary time-series are as follows:
12, 14, 13, 10, 15, 12, 15
(a) Calculate auto-covariances C0, C1, C2, C3 and C4.
(b) Calculate auto-correlation coefficients r1, r2, r3 and r4.
(c) Plot the correlogram.
Four professors are capable of teaching any one of four different courses. Class preparation time in hours for different topics varies from professor to professor and is given in the table below:
| Professor | A | B | C | D |
|---|---|---|---|---|
| Linear Programming | 2 | 15 | 13 | 4 |
| Queuing Theory | 10 | 4 | 14 | 15 |
| Transportation Problem | 9 | 14 | 16 | 13 |
| Regression Analysis | 7 | 8 | 11 | 9 |