Question

derive the regression line,y’= a+bX for the data below.After you have calculated the regression equation,explain to me how you could use it.

                               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

The following data are passed:

Advertising Expenditure (in Millions of $)	Sales Revenue (in Millions of $)
1	3
2	7
3	5
4	11
5	14

The independent variable is \(Advertising Expenditure (in Millions of $)\), and the dependent variable is \(Sales Revenue (in Millions of $)\). In order to compute the regression coefficients, the following table needs to be used:

	Advertising Expenditure (in Millions of $)	Sales Revenue (in Millions of $)	Advertising Expenditure (in Millions of $)*Sales Revenue (in Millions of $)	Advertising Expenditure (in Millions of $)2	Sales Revenue (in Millions of $)2
	1	3	3	1	9
	2	7	14	4	49
	3	5	15	9	25
	4	11	44	16	121
	5	14	70	25	196
Sum =	15	40	146	55	400

Based on the above table, the following is calculated:

Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows:

Therefore, we find that the regression equation is:

Sales Revenue (in Millions of $) = 0.2 + 2.6 Advertising Expenditure (in Millions of $)

As the equation is obtained we can obtain Sales Revenue in coming months based on this