business statistics ppt

8/13/2019 Business Statistics Ppt

1/19

Business StatisticsCorrelation

6thSeptember, 2013

Group No.11


2/19

Introduction

Correlation is technique used to measure

relationship between to variables or

more Correlation analysis shows us how to

determine the nature & strength of

relationship between two variables


3/19

Correlation Range

Correlation lies between +1 to -1

Zero correlationNeutral (No relationship )

-1 correlation Perfect -ve (Very Weak)

+1 correlation Perfect +ve (Very Strong)


4/19

Types of Correlation

Karl Pearsons Coeff is denoted by r

Spearmans Rank is denoted by

Correlation

Direct (Quantitative)

Eg. Price Demand

Ads Sales

Karl Pearsons Coeff

Partial (Qualitative)

Eg. Demand Income

Spearmans Rank Coeff


5/19

Karl Pearson's correlation

Karl Pearson's coefficient of correlation

is the measure of the strength of linear

dependence between two variables.

It is also called as Pearson's product-

moment correlation coefficient.

It is denotedby r.

Its value always lies between -1 and +1.


6/19

It is given by the formula


7/19

example

student Height in cm(x)

Weight(y)

x y xy

1 150 45 22500 2025 6750

2 155 50 24025 2500 7750

3 160 55 25600 3025 8800

4 165 60 27225 3600 9900

5 170 65 28900 4225 11050

sum 800 275 128250 15375 44250


8/19

Application

()( )

[" (" ) )][ ()]

= 1250

1250 1250

= 1250 = 1

1250


9/19

INTERPRETATION

r= 0.5 moderate +ve correlation

r=0.6 good +ve correlation

r=0.8 strong +ve correlation.

r=0.9/more spurious +ve correlation.


10/19

Spearmans Rank Correlation

Coefficient

Spearmans correlation coefficient is used for

qualitative data.

It measures the strength of association

between two rankedvariables.

It is the nonparametric(distribution-free)

version of the Pearson product-moment

correlation.


11/19

It is given by the formula

Where

di= difference in paired ranks

n= number of cases


12/19

Ranking the data

Given data-

English 56 75 45 71 61 64 58 80 76 61

Maths 66 70 40 60 65 56 59 77 67 63


13/19

RANK

English

(mark)

Maths

(mark)

Rank

(English)

Rank

(maths)

56 66 9 4

75 70 3 2

45 40 10 1071 60 4 7

61 65 6.5 5

64 56 5 9

58 59 8 8

80 77 1 1

76 67 2 3

61 63 6.5 6


14/19

English

(mark)

Maths

(mark)

Rank

(English)

Rank

(maths)d d2

56 66 9 4 5 25

75 70 3 2 1 1

45 40 10 10 0 0

71 60 4 7 3 9

62 65 6.5 5 1 164 56 5 9 4 16

58 59 8 8 0 0

80 77 1 1 0 0

76 67 2 3 1 1

61 63 6.5 6 1 1

We then complete the following table:

Where d = difference between ranks and d2= difference

squared.


15/19

We then calculate the following:

We then substitute this into the main equation with the other information as

follows:


16/19

Interpretation

In a sample it is denoted by or rsand liesbetween:

-1


17/19

Some Real Life Examples

Rainfall and absenteeism -example of positive correlation

Age and sleep-example of negative correlation The size of your palm is negatively correlated with how long you

will live. In fact, women tend to have smaller palms and live longer.

As the ocean level falls, the fish population size decreases. Heavy traffic correlates with the time of day.

There is heavy traffic between 8:00 AM and 9:00 AM andagain between 4:30 PM and 6:00 PM

An increase in the rate of inflation causes goods to be more

difficult to purchase, all other factorsremaining unchanged;


18/19

Application 1:

The local ice cream shop keeps track of how much ice creamthey sell versus the temperature on that day, here are theirfigures for the last 12 days:

You can easily see that warmer weather leads to moresales, the relationship is good but not perfect.

Correlation is 0.968721

Ice Cream Sales vs Temperature

Temperature in Degrees Ice Cream Sales(in thousand)

14.2 14

15.2 22

22.1 34.5

25.1 40.6

17.2 27


19/19

business statistics ppt

Documents