Problem 5(10) Jones Corp. has noticed that sales of its product seem to be influ

Question

Problem 5(10) Jones Corp. has noticed that sales of its product seem to be influenced by a variable it calls Gamma. It has developed the data shown in the following table. GammaSls Gamma x Sales Gamma 10 22 220 34 612 26 364 30 420 24 288 100 324 196 196 144 960 Total Average 13.6 1904 27.2 Develop a simple linear regression from the data and tell Jones what the sales forecast will be if Jones expects "Gamma" to be 16. 1. Define an independent variable and a dependent variable. 2. Find a lincar regression model. 3. Find the forecasted sales when "Gamma" is 16.

Explanation / Answer

5.

1.

Dependent variable = Y = Sales

Independent variable = X = Gama

2.

Linear regression model will be as follows:

Sales = a + b*Gama

Or

Y = a + b*X

b = (n?xy -?x * ?y)/(n?x^2 - (?x)^2)

b = (5*1904 - 68*136)/(5*960 - 68^2)

b = 1.5455

a = (?y – b*?x)/n

a = (136 - 1.5455*68)/5

a = 6.18

So,

Y = 6.18 + 1.5455*X

Or

Sales = 6.18 + 1.5455*Gamma

3.

When Gamma is 16,

Then

Forecasted sales = 6.18 + 1.5455*16 = 30.90 or 31

Gamma (X) Sales (Y) Gama*sales Gamma^2 10 22 220 100 18 34 612 324 14 26 364 196 14 30 420 196 12 24 288 144 Total= 68 136 1904 960

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.