Question

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

Month Number of Oil Changes January 48 February 43 March 49 April 51 May 57 June 58 July 62 August 67

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

Month period(X) number of oil changes(Y) XY X^2

Jan 1 48 48 1

Feb 2 43 86 4

Mar 3 49 147 9

Apr 4 51 204 16

May 5 57 285 25

June 6 58 348 36

July 7 62 434 49

Aug 8 67 536 64

X = 1+2+3+4+5+6+7+8 = 36

Y = 48+43+49+51+57+58+62+67 = 435

XY = 48+86+147+204+285+348+434+536 = 2088

X^2 = 1+4+9+16+25+36+49+64 = 204

Number of periods = n = 8

X-bar = X/n = 36/8 = 4.5

Y-bar = Y /n = 435/8 = 54.38

b = [XY - (n. X-bar. Y-bar)] /[X^2 - (n. Square of X-bar)]

= [2088-(8 x 4.5 x 54.38)] / [204-(8 x 4.5 x 4.5)]

= (2088 - 1957.68)/(204-162)

= 130.32/42

= 3.10

a= Y-bar - (b. X-bar) = 54.38 - (3.10 x 4.5) = 54.38-13.95 = 40.43

So the regression equation is Y = a + bx => Y = 40.43+3.10x