Problem 5(10) Jones Corp. has noticed that sales of its product seem to be influ
ID: 327680 • Letter: P
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