Question

Correlation(Part 1)-Week 11 -compute r,r2 and 1-r2 for the problem below .What does r,r2 and 1-r2 mean ? Is the correlation strong or weak ?

You are given the following data:

   X(Independent Variable) Y(Dependent variable)

Month Advertising Expenditure (in Millions of $) Sales Revenue (in Millions of $)

July 1 3

August 2 7

September 3 5

October 4 11

November 5 14

Answer 1

Let x = Independent variables = Advertising Expenditure (in Millions of $) and

y = dependent variables = Sales Revenue (in Millions of $) .

correlation coefficient (r) is used to measure the linear relationship between two variables

Here we want to find the correlation coefficient (r)

correlation coefficient (r) can be calculated as

Sr. No.	Month	Advertising(x)	Sales(Y)	(x-xbar)	(y-ybar)	(x-xbar)^2	(y-ybar)^2	(x-xbar)*(y-ybar)	(x-xbar)^2*(y-ybar)^2
1	July	1	3	-2	-5	4	25	10	100
2	Aug	2	7	-1	-1	1	1	1	1
3	Sept	3	5	0	-3	0	9	0	0
4	Oct	4	11	1	3	1	9	3	9
5	Nov	5	14	2	6	4	36	12	144
	Mean	3	8		Total	10	80	26

we get

  

we get the correlation coefficient(r) = 0.9192 ..................(ANSWER)

Interpretation: There is strong positive correlation between advertising Expenditure (in Millions of $) and Sales Revenue (in Millions of $) .

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2) Coefficient of Determination(): It is proportion of total variation in Sales Revenue (in Millions of $) explained by advertising Expenditure (in Millions of $)

Coefficient of Determination() is calculated as

.................(ANSWER)

Interpretation: 84.50% variation in Sales Revenue (in Millions of $) explained by advertising Expenditure (in Millions of $)

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3) we want to find

i.e. .................(ANSWER)