Question

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

                                                                 

Month	Number of Oil Changes
January	33
February	53
March	56
April	58
May	69
June	46
July	62
August	69

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 X=​1; for​ February, let X=​2; and so on.

The forecasting model is given by the equation Y =4 0.86 +3.31X.

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

b. Use the model to forecast demand for​ September, October, and November.​ Here,

X=​9, ​10, and​ 11, respectively. ​(Enter your responses rounded to two decimal​ places.)

Month	Forecast for the number of Oil Changes
September
October
November

Answer 1

PERIOD (X)	DEMAND (Y)	X	Y	X * Y	X^2
1	33	1	33	33	1
2	53	2	53	106	4
3	56	3	56	168	9
4	58	4	58	232	16
5	69	5	69	345	25
6	46	6	46	276	36
7	62	7	62	434	49
8	69	8	69	552	64
SIGMA		36	446	2146	204

INTERCEPT = (SIGMA(Y) * SIGMA(X^2) - SIGMA(X) * SIGMA(XY)) / (N * SIGMA(X^2) - SIGMA(X)^2)

INTERCEPT = (446 * 204) - (36 * 2146) / ((8 * 204) - 36^2) = 40.86

SLOPE = ((N * SIGMA(XY)) - (SIGMA(X) * SIGMA(Y))) - (N * SIGMA(X^2) - SIGMA(X)^2)

SLOPE = ((8 * 2146) - (36 * 446) / ((8 * 204) - 36^2) = 3.31

Y = A + B(x), WHERE A IS THE INTERCEPT, B IS THE SLOPE, x IS THE PERIOD = 40.86 + (3.31 * X)

FOR THE VALUE OF X = 9 FORECAST = 40.86 + (3.31 * 9) = 70.65

FOR THE VALUE OF X = 10 FORECAST = 40.86 + (3.31 * 10) = 73.96

FOR THE VALUE OF X = 11 FORECAST = 40.86 + (3.31 * 11) = 77.27

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