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Simple and Multiple Linear Regression Analysis Sample Assignment

Questions: Give σx = 3 and Regression equation 8X – 10Y + 66 = 0; 40X – 18Y = 214.
Find Out (i) The mean value of X and Y, (ii) Coefficient of correlation between X and Y and (iii) Standard deviation of Y.

Sol: (i) We know, the two regression lines intersect each other at the mean values of X and Y. Therefore, these values can be obtained by solving these two regression equations 8X – 10Y + 66 = 0; 40 X – 18Y = 214

or    8X – 10Y = – 6 
    40 X – 18Y = 214

Multiplying equations (i) by 5, we have

40X – 50Y = –330
40 X – 18Y = 214
_-_    +  ___  -   
 -32 Y = -544
or     Y = +544 = 17
                +32
Y = 17

By substituting the value of Y in equation (i),

8X – 10(17) = – 66
or     8X = – 66 + 170
or    8X = 104
    X = 13 or
    X = 13

(ii) In order to determine the correlation coefficient, we will have to find out regression coefficients. Here, we do not know which of the two regression equation (i) as regression equation X on Y.
Given equation is

8X – 10Y + 66 = 0

Or 8X – 10Y = – 66

or X = 10Y/8 – 66/8

or X = 10/8 (Y – 6.6)

.: bxy = 10/8 = +1.25.

From equation (ii)

40X – 18Y = 214

or 18Y = 40X – 214

or Y = 40X/18 – 214/18

.: b_yx = 40/18 + 2.22.

Since the product of these two regression coefficients (i.e., b_xy x b_yx = 1.25 X 2.2) is exceeding one, our assumption is wrong. Therefore, first equation is Y on X and the second X on Y.

.: 8X – 10Y + 66 = 0

or 10Y = 8X +66 = 0

or Y = 8X + 66
        10
or Y = 8/10 (X + 52.8)
.: Y = 8/10 + .8

From equation (ii)

40X – 18Y = 214
40X = 214 + 18Y

X = 18Y + 214
        40       40
or X = 18/40Y + 5.35
.: b_xy = 18/40 = +0.45
.: r = √(b_xy x b_yx)
.: σ_y = 4

Other Sample Assignments in Statistics Homework Assignment :

Continious Distribution	Descrete Distributions
Descriptive Statistics	Nonparamatric Statistics
Probability	Sampling And Sampling Distribution
Statistical Inference Estimation For Single Popula	Simple Regression Analysis
Statistical Inference About 2 Population	Time Series Forcasting Index Number
Statistical Quality Control	Correlation
Index Number	Larger Sample Mean Proportions
Non Parametric Test	Probability Theory
Sampling Distribution	Simple and Multiple Linear Regression Analysis
Unvariate Analysis

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