Question

Demand for oil changes at​ Garcia's Garage has been as​ follows:

                                                                 

Month	Number of Oil Changes
January	47
February	41
March	63
April	47
May	57
June	44
July	52
August	71

a. Use simple linear regression analysis to develop a forecasting model for monthly demand. In this​ application, the dependent​ variable, Y, is monthly demand and the independent​ variable, X, is the month. For​ January, let

Xequals=​1;

for​ February, let

Xequals=​2;

and so on.

The forecasting model is given by the equation

Yequals=nothingplus+nothingX.

​(Enter your responses rounded to two decimal​ places.)

Answer 1

Answer:

Step 1: Let X = Independent Variable = No. of a particular Month, and Y = Dependent Variable = Monthly Demand

Then, prepare the following table:

Step 2: Find the colums of xy, x^2, and y^2

Where xy = x*y

x^2 = x*x

y^2 = y*y

Hence, we get,

Step 3: Find the values of 'a' as mentioned below:

= (86088 - 71532) / (1632-1296)

= 14556 / 336

= 43.32 (Rounded to 2 Decimal Places)

Step 4: Find the values of 'b' as mentioned below:

= (15896-15192) / (1632-1296)

= 704 / 336

= 2.10 (Rounded to 2 decimal places)

Step 5: FInd the linear equation

Y = a + b X

Hence, we get the linear equation model = Y = 43.32 + 2.10 X