Question

Demand for oil changes at Garcia’s Garage has been as follows: Month Number of Oil Changes January 41 February 46 March 57 April 52 May 59 June 51 July 60 August 62 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 X=1; for February, let X = 2 X=2; and so on. Use the model to forecast demand for September, October, and November. Here, X = 9 , 10 X=9,10, and 11, respectively. I have the answers, but I need to elaborate on how they relate to linear regression as well. Some written material on the matter.

Answer 1

The regression analysis is a popular approach to forecasting. Especially if there is a trend (increasing or decreasing) then the linear regression approach can provide considerably better result than other methods.

In this case we can see that there is a clear increasing (upward) trend in the demand data for Garcia’s Garage. This means that most likely the next months will see increased demand. However, in order to forecast that we need to determine the trend. This is where linear regression is helpful. They provide a way to find the equation of the line that has least amount of squared error between the points. As a result, the linear regression line is the best fit line that is possible for months January through August. This also means that in all likelihood, the line may be very close to the demand.

The regression analysis is also shown in the image and we can see that as per the regression analysis, the equation is

Forecasted demand = 42.46 + 2.45*Month

P.S. Not providing the values for September, October and November since you already have the answer for that.