Question

Assignment # 2 Management Economics

Simple Regression

Using as a guide question 1 of the applications section of unit 2 of the course content and the following table of sales department data:

Years	Sales(000)	Advertising($1000)
1	10	1
2	20	2
3	40	3
4	50	4
5	60	6
6	80	7
7	90	8

We know that in the simple regression the independent variable is one (that's why it's simple)

After analyzing the table we clearly see that sales increase as advertising increases.

Question 1) Between sales and advertising, what is the dependent variable, and which one is independent?

Information:

The formula to use in simple linear regression is as follows:

Y = a + bx

Where:

y = dependent variable or value expected at the end of the analysis

a = represents the intercept or value of the point where the drawn edge intercepts or crosses the vertical axis

b = represents the slope or inclination of the line drawn

x = independent variable

n = to # of periods in this case 7

A b and a have to calculate their independent value to determine Y

b = (nΣxy- ΣxΣy) / (nΣx²- (∑x) ²) a = (Σy- bΣx) / n

In order to substitute the variables of the formula we have to

Know how much xy is and how much is X²

Question 2: take the value of xy and that of x² in the table below and then solve the summations of

Sales, advertising, XY, X²

Year	Sales (000)	Advertising($000)	XY	x²
1	10	1
2	20	2
3	40	3
4	50	4
5	60	6
6	80	7
7	90	8
N=7	∑y=	∑x=	∑xy=	∑x²=

Question 3: Determine the value of a and the value of b (use the formulas given above for a and b) and then determine the value of Y

Question 4: If the advertising expense were $ 15,000, what would be the expected sale?

Answer 1

Ans 1) Dependent Variable is Sales

Independent Variable is Advertising

Explanation: Sales depend on the advertising Expense

Ans 2)

Year	Sales(y)	Advertising(x)	xy	x2
1	10	1	10	1
2	20	2	40	4
3	40	3	120	9
4	50	4	200	16
5	60	6	360	36
6	80	7	560	49
7	90	8	720	64
N = 7	∑y= 350	∑x= 31	∑xy= 2010	∑x²= 179

Ans 3)

Y = 1.164 + 11.0274x ans.

Ans 4) Given x = 15000

Y(Sales) = 1.164 + 11.0274*15000 = 1.164 + 165411 = 165412.2 ans.

Expected sale = $165412.2