Description

(Timely submission of assignments is essential. Copying/plagiarised submission from
others will fetch fail (F) grade on this subject)

1. Annual Revenue data for a company is given as,

Rev.
In billion
Rupe
es 61.2 58.3 67.1 69.2 68.9 83.5 89.1 80 92.3 93 97

a) Draw a least square line fitting the data.
c) Analyze expected error in predictions. 10

2. The following table shows the final semester marks obtained by 10 students selected at random.

M L 75 80 93 65 87 71 98 68 84 77
HUR 82 78 86 72 91 80 95 72 89 74

Find least square line fitting the above data using
a) X as independent variables (regression of Y on X)
b) Y as independent variable (regression of X on Y)
c) If a student receives a mark 96 in ML, what is her/his expected marks in HUR.
d) If a student receives 95 in HUR. What is her/his expected marks in ML.
e) After plotting a) and b) what conclusions can you draw? 10

3. Experimental results of pressure (P) for a given mass of gas corresponding to various values of volume (V) is given as:

V 54.3 61.8 72.4 88.7 118.6 194
P 61.2 49.5 37.5 28.4 19.2 10.1

n
Assume PV = const =c
a) Find the parameters n and c
b) Write the equation connecting P and V.
c) Estimate the value of P when V=100
10
4. Find the least square parabola which fits the data
Y= W0 + W1X+ W2 X^2
X 0 1 2 3 4 5 6
Y 2.4 2.1 3.2 5.6 9.3 14.6 21.9

:
a) Normal equations with and without regularization and compare their performances in terms of % error in prediction. ( only allowed to use NumPy library of Python.no other functions/libraries are allowed )

b) Design Predictor using Batch Gradient Descent Algorithm, Stochastic Gradient Algorithm and mini batch Gradient Descent algorithms (determining minibatch size is your choice- here it could be 10, 20, 30 etc.) with and without feature scaling and compare their performances in terms of % error in prediction.(only allowed to use NumPy library of Python, no other functions/libraries are allowed)

c) Design Predictor using Batch Gradient Descent Algorithm, Stochastic Gradient Algorithm and mini batch Gradient Descent algorithms (determining minibatch size is your choice- here it could be 10, 20, 30 etc.) with and without regularization and compare their performances in terms of % error in prediction.(only allowed to use the NumPy library of Python, no other functions/libraries are allowed) ( ref Lecture-10, 11 and 12)

d) Implement the LWR algorithm on the Housing Price data set with different tau values. Find out the tau value which will provide the best fit predictor and hence compare its results with a) , b) and c) above. 50

All assignments given before C-1 evaluation, will be counted towards C-1 marks.