Download - Correlation vs. Regression
Correlation analysis-meaning & types of correlation, Karl Person’s coefficient of correlation and spearman’s rank correlation; regression analysis- meaning and two lines of regression; relationship between correlation and regression co-efficient. Times series analysis- measurement of trend and seasonal variations; time series and forecasting.
Unit 2
A S Raheja
9717871155
Correlation vs. Regression
Examples Price and supply
Income & Expenditure
Correlation analysis is used to measure strength of the association (linear relationship) between two variables Correlation is only concerned with strength of the relationship.
No causal effect is implied with correlation.
Most widely used and widely abused statistical measure.
Reduces range of uncertainty.
Types of Correlations
Issues with Correlation Chance Coincidence Influence of one on other or mutual dependence Both being influenced by third variable
Methods Scatter diagram Karl Pearson’s Coefficient of Correlation Rank Method
Scatter Diagram
Y
Y
X
Non Linear correlation
X
Y
X
Y
X
+ Correlation, r>0
- Correlation, r<0 No Correlation, r = 0
Type of Correlation
A measure of the linear association between variables – Positive Correlation indicates positive linear relationship – Negative Correlation indicates a negative linear
relationship – Values close to zero indicates no linear relationship
It not affected by the units of measurement for x and y variables – Pearson product moment correlation coefficient or Sample
correlation coefficient, r (used in case data is continuous) It is a numerical index that reflects the linear relationship between two
variables The values of the descriptive statistic range between a value -1 (perfect –ve
correlation) to +1(perfect positive correlation) , it is also referred to as Bi variate
Correlation Formula 1
Wherer = sample correlation coefficient,σxy = sample covarianceσx = sample standard deviation of xσy = sample standard deviation of y
yx
xy
xyr ))((
1 __
YYXXnXY
)(21
XXnx )(
21YYny
Calculating from Covariance
Knowing the covariance and the standard deviations of each variable we can compute the sample correlation coefficient, r
Covariance = 11, σx = 1.49, σy = 7.93
So Pearson r = 11/(1.49 x 7.93) = 0.93
Correlation Formula 2
2222 )(1
)(1
.1
Yn
YXn
X
YXn
XYr
Solution
Assumed mean
2222 )(1
)(1
.1
yn
yxn
x
yxn
xyr
bYy
aXx
Spearman’s Rank Correlation
On some occasion it is not possible to measure the variables quantitatively or exact magnitude of the variable can not be determined Numerical value of beauty Measure taste of wine
)1(
61
2
2
NNr Ds
Rules
When Rank are given – above formula is sufficient When Ranks are not given – ranks are assigned by taking either the
highest value as 1 or the lowest value as 1 Equal Ranks- in some cases, rank may be equal , in such case each
individual is given an average rank
Exercise 1
Exercise 2
Exercise 3