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Detailed informtion about BIVARIATE DATA ANALYSES, Correlation Coefficient, PARTIAL CORRELATION COEFFICIENT, LINEAR relation ,Explaination.
Typology: Lecture notes
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Is there an association between market share and size of
sales force where hard selling is concerned?
Are consumers' perceptions of quality related to their
perceptions of prices?
Can coverage of miles be a good judge of the resale value
of a used car?
How are the prices and demands of different commodities
related?
Is there any significant association between performance
and confidence?
Association – Correlation Coefficient
Correlation Coefficient (r) is a statistic summarising the
strength and direction of association between two metric
(interval or ratio scaled) variables
-1 r 1
r is an absolute number
r is a symmetric measure of association
r measures the strength of linear relationship
r measures the direction of linear relationship
Correlation is 0.603 (based on 20 observations)
Correlation is 0.893 (based on 20 observations)
(Very high correlation, quite close to 1.0)
1
2
2
= c - dX
1
r (X
1
2
1
= a - bX
2
How strongly are sales related to advertising expenditures when
the effect of price is controlled?
Is there an association between market share and size of the sales
force after adjusting for the effect of sales promotions?
Are consumers' perceptions of quality related to their perceptions
of prices when the effect of brand image is controlled?
Temperature affects both rainfall and yield of crop; how does one
find the true relation between rainfall and yield of crop?
Partial Correlation Coefficient (also known as coefficient of partial
determination), r
xy.z
is a measure of association between two
variables after controlling or adjusting for the effects of one or more
additional variables.
(n+1)th order Partial Correlation Coefficient is obtained by
replacing simple Correlation Coefficient in equation (1) by the nth
order Partial Correlation Coefficient.
and r
12
need not have the same sign
13
= 0 and r
23
= 0, does it mean that r
12
= 0 also?
Ex 1) In software profession does performance improve with age?
1
= performance, X
2
= age, X
3
= professional experience
r
12
= 0.61, r
13
= 0.82, r
23
=> r
= - 0.0357 => r
12
= 0.61 is not the true picture.
If the effect of professional experience is controlled, performance
actually diminishes with age !!!
Because, ‘professional experience’ is highly correlated with
Ex.2) X
1
= sales, X
2
= advertising expenditure,
3
= size of sales force,
r
12
= 0.9361, r
23
= 0.5495, r
13
=> r
= 0.9386 => Sales and advertising expenditure are related;
r
12
= 0.9361 This relation is NOT due to the effect of size of
sales force on each of them
Ex.3) X
1
Consumption of basic amenities of life,
2
Income, X
3
Household size
r
12
= 0.48, r
23
= 0.54, r
13
=> r
=>Correlation between income and consumption is spurious
