Coding

It's only fair to share...Share on FacebookTweet about this on TwitterPin on PinterestShare on Google+Share on RedditEmail this to someone

Coding is a method of transforming data so that the numbers are easier to manipulate. Numbers that are not too small and not too large are easier to work with, so if the raw data we start with consists of large numbers for example – and finding the standard deviation or variance will make them even larger, since we must find – we may wish to make them smaller using a coding relationship of the form andwhereandare the original data and andthe transformed data. We can then do the calculations, finding the correlation coefficient, the equation of the regression line for the transformed data. We have to transform back to the original variablesandusing the original coding relationship. The correlation coefficient is unaltered- the correlation coefficient for the relationship betweenandis the same as that for the relationship betweenand

Example: A company owns two petrol stationsandalong a main road. Total daily sales in the same week for) and for) are summarised in the table below.

£

£

Monday

4760

5380

Tuesday

5395

4460

Wednesday

5840

4640

Thursday

4650

5450

Friday

5365

4340

Saturday

4990

5550

Sunday

4365

5840

The data are coded using the relationshipandobtaining the new table below.

P

q

Monday

3.95

1.04

Tuesday

1.03

1.2

Wednesday

1.475

3

Thursday

2.85

1.11

Friday

10

0

Saturday

6.25

1.21

Sunday

0

1.5

The summary statistics for the table above are:

where

SoWe have to transform back to the original variablesand

Rearrangement of this equation givesThe negative sign means the two petrol stations are partially in competition – if one sells more, the other sells less.

Comments are closed.