1. MARKETING - UTOPIA
REGRESSION (IN BUSINESS RESEARCH)
A regression is a statistical analysis assessing the association between two
variables. It is used to find the relationship between two variables.
Usually, the investigator seeks to ascertain the casual effect of one variable upon
another-the effect of a price increase upon demand, for example, or the effect of
changes in the money supply upon the inflation rate.
Regression Equation
=a+bx
Example: A farmer wised to know how many Kg of Rice would result from
application of 20 pounds of Euria.
The 20 pound of Euria is the X or value of the predictor variable. The predicted Kg
of rice would be y or the predicted value of the criterion variable.
Using the example we begun in correlation:
Pounds of Euria (X) Kg of Rice (y)
Table of Regression
X (X- ) (X- )2 y (y- ) (y- )2 (X- ) (y- )
10 -40 1600 30 -20 400 800
20 -30 900 40 -10 100 300
50 0 0 50 0 0 0
70 20 400 60 10 100 200
100 50 2500 70 20 400 1000
250 0 5400 250 0 1000 2300
=50 =50
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Co-relation
r=
=
= .99
We calculate the components of the regression equation beginning with b.
b= = = .43
Slope of regression
number
This gives us the slope of the regression line. For each 1.00 increment increase in
x, we have a 0.43 increase in y. next, we calculate a.
a = - b = 50 – (43)(50) = 28.5
If we wish to know how much more rice to expect from a 35 pound application of
Euria, we calculate:
= a+b (35) Y tau is the true
value of x and y.
= 28.5 + .43 (35)
= 28.5 + 15.05
= 43.6 expected bushels of corn
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STANDARD ERROR
The approximate value of the standard error of the estimate tells us the accuracy
to expect from our prediction. The standard error for the estimate is calculated by
the following formula:
–
Syx =
Total number of respondent
The formula may look formidable, but we already have calculated all of the
components except for sharing the :-
STANDARD ERROR CALCULATION
Syx = = = = 2.6
Error in the regression
Total number of respondent
This approximate value for the standard error of the estimate tells us the accuracy
to expect from our prediction. Thus, for our prediction of 43.6 Kg from an
application of 35 pounds of Euria, we can expect to predict a yield varying from 41
to 46.2 Kg with approximately 68% accuracy, to predict a yield varying from 38.4
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to 48.8 with approximately 95% accuracy, or to predict a yield varying from 35.8
to 51.4 with 99% accuracy.
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