Question

The following table presents the orders of Samson Company for the last 36 months (3 years).

Month	Order Year 1	Order Year 2	Order Year 3
January	502	614	712
February	408	592	698
March	491	584	686
April	456	532	644
May	481	599	694
June	511	604	702
July	522	624	724
August	500	612	716
September	510	625	732
October	512	627	740
November	520	650	745
December	536	680	756

1. Use the data in the above table and regression analysis to forecast the orders for the next 12 months (4th year). Include your excel work sheet and your write up. Show the regression equation, values of intercept, slope, correlation coefficient and coefficient determination and the forecast of orders for the next 12 months.

2. Explain how you could make your forecast’s results more reliable by incorporating a qualitative research to your quantitative results.

Answer 1

1:- As we don’t have enough information regarding the data so it would be best to run a simple linear regression model considering time point as the independent variable.

Due to limited information of the presented data, we would like to run a simple linear regression model assuming time point as the independent variable.

Let

Time = 1 for Year 1 January;

= 2 for year 1 February;

.. and so and regress the “Number of orders” on this time points.

The obtained regression output is given below.

The above output is indicating that the correlation coefficient is 0.9664 indicating a strong positive linear association between the variables. The coefficient of determination is 0.9339, thus 93.39% of the variation in the “number of orders” is getting explained by the variation in the “Time Point”. The intercept and slope coefficients are 444.4254 and 8.7713 respectively so the regression equation is,

Number of orders = 444.4254+8.7713*Time Point

As the regression model is significant (p-value < 0.0001) so this model can be used to predict the future values.

Now, the time point value for Year 4, January is 37, for February it is 38 and so on. Using these values and the above regression model we have the following values as the forecast for the number of orders in Year 4.

Year 4	Time Point	Number of orders
January	37	768.96
February	38	777.73
March	39	786.51
April	40	795.28
May	41	804.05
June	42	812.82
July	43	821.59
August	44	830.36
September	45	839.13
October	46	847.91
November	47	856.68
December	48	865.45

2:- This forecasting is helping us to predict the unknown future from the past data. Higher accuracy in the prediction can be obtained by having more data and by implementing this fact, the reliability of the quantitative results can be boosted by the qualitative research. The forecasting becomes more efficient with the help of qualitative research like the type of the product, the market structure, the number of competitors, seasonality, any important upcoming event etc. If these research data can be used in the quantitative analysis somehow, it will yield greater accuracy and reliability.