Question

The Owner of WOW Furniture studio wants to know the relationship between sales and the amount he spent on digital advertising. The sales information for the last four months is repeated below:

Month	Advertising Expense (Millions)	Sales Expense (millions)
July	2	7
August	1	3
September	3	8
October	4	10

A) Determine the regression equation Answer:

b =

a =

B) Interpret the values ​​of a and b (fill the blank)
The slope is _____ This indicates that _________ of a million in advertising will generate a ____________ of 2.2 million in sales. The intersection is _______, if there were no advertising expenses, sales would be __________ million.

C) Estimate sales when they spend 3 million on digital advertising

R:

Answer 1

Let Yi denote Sales and Xi denote Advertising expense.

We have to estimate the equation Yi= a+ bXi

where a is the intercept and b is the slope coefficient.

OLS regression is used to estimate the equation.

Yi (Sales Expense)	Xi (Advertising expense)			xiyi
7	2	0	-0.5	0	0.25
3	1	-4	-1.5	6	2.25
8	3	1	0.5	0.5	0.25
10	4	3	1.5	4.5	2.25

yi & xi is the mean deviation of individual values from the mean value.

where, is the mean value of Yi

where, is the mean value of Xi

= 7+3+8+10/4= 7

= 2+1+3+4/4= 2.5

According to OLS regression,

b= 11/5= 2.2

a= 7-2.2(2.5)= 1.5

The estimated equation is Yi= 1.5+2.2(Xi)

Thus, a=1.5, b=2.2

B) The slope is b=2.2. This indicates that increase of a million in advertising will generate a increase of 2.2 million in sales. The intersection is a=1.5, if there were no advertising expenses, sales would be 1.5 million.

C) Digital advertising=3 million

Xi= 3

Substitute this value in the equation Yi= 1.5+2.2(Xi)

Yi= 1.5+2.2(3)= 8.1

The sales will be 8.1 million.