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

asraheja@gmail.com

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