Question

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

                                                                 

Month	Number of Oil Changes
January	43
February	51
March	63
April	50
May	60
June	42
July	68
August	72

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=+X.

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

Answer 1

PERIOD	DEMAND	X	Y	XY	X^2
1	43	1	43	43	1
2	51	2	51	102	4
3	63	3	63	189	9
4	50	4	50	200	16
5	60	5	60	300	25
6	42	6	42	252	36
7	68	7	68	476	49
8	72	8	72	576	64
SIGMA		36	449	2138	204

INTERCEPT(B0) = (SIGMA(Y) * SIGMA(X^2) - SIGMA(X) * SIGMA(XY)) / (N * SIGMA(X^2) - SIGMA(X)^2)

INTERCEPT = (449 * 204) - (36 * 2138) / ((8 * 204) - 36^2) = 43.54

SLOPE(B1) = ((N * SIGMA(XY)) - (SIGMA(X) * SIGMA(Y))) - (N * SIGMA(X^2) - SIGMA(X)^2)

SLOPE = ((8 * 2138) - (36 * 449) / ((8 * 204) - 36^2) = 2.8

EQUATION

Y = INTERCEPT + SLOPE(X)

Y = 43.54 + (2.8 * (X))

FOR X = 9(SEPTEMBER), FORECAST = 43.54 + (2.8 * 9) = 68.74