Prepare Paul Jordan’s report to John Smithers using regression analysis. Provide a summary of the cell phone industry outlook as part of Paul’s response.
Digital Cell Phone Inc requires the forecasted sales of the next 12 months in order to plan the production and avoid too much or too few inventory of cell Phones. In order to forecast the sales of the cell phones, a regression analysis needs to be done.
There has been used linear regression for forecasting sales. First of all, number the months from 1 to 36 for the three years. This will be the independent variable represented by “Month”. The dependent variables are the sales of these months and are represented as “Sales”. Assuming no seasonality, regression is done on the three years sales data. The equation of the line of best fit is as follows:
Plagiarism Free Work
Best Price Guarantee
100% Money Back Guarantee
Top Quality Work
Sales = 5.248 Month + 440.859
The coefficient of months is statistically significant which means that the sales are affected by the month, and that equation can be used for forecasting. The equation shows an upward trend of the sales of cell phones based on the last three years sales data. Exhibit 1 shows the forecast using the above equation. The forecast shows increasing sales as predicted. As seasonality is not accounted for, the forecast shows a rise in sales each month by almost the similar amount.
Adding seasonality into your model, how does the analysis change?
From the above regression equation, a continuous growth in the cell phone industry is anticipated for the next 12 months. However, Jordan should inform his boss that it would be wise to stray away from these forecasts in certain months due to the seasonality affect on sales. In certain months during the years, the sales are lower than usual while in other months, the sales are higher than usual.
Hence, in order to account for the seasonality affect, a seasonality factor needs to be added to the regression equation. The given data shows seasonal variations as there exists regular up and down fluctuations in a time series which might relate to recurring events such as the holiday season.
To add seasonality to the equation, four dummy variables are first defined; Q1, Q2, Q3 and Q4. Q1 is a dummy variable that is 1 for the first quarter, i.e. January, February and March, and otherwise it is 0. Similarly, Q2 is 1 for the second quarter, Q3 for the third quarter and Q4 for the fourth quarter.
For the regression, the dependent variable is “Sales” while the independent variables are the “Month”, “Q1”, “Q2”, and “Q3”. Q4 is not included in regression because it would become redundant. When Q1, Q2 and Q3 are all zero the value of sales is for Q4. The regression equation accounting for seasonality is shown below:
Sales = 429.367 + 5.689 Month + 30.649 Q1+ 8.803 Q2 – 26.154 Q3
The equation shows an upward trend for sales as before. However, in the third quarter the sales will be lower than the other months due to the negative coefficient. Exhibit 1 shows the forecast after incorporating seasonality. The Exhibit also shows the difference between the two estimates.
It is obvious that forecast with seasonality shows higher sales than forecasts without seasonality except in the third quarter sales forecast of July, August and September. Overall, the new forecast shows an upward trend as before, despite the seasonality. Furthermore, new equation also has a statistically significant positive coefficient for “Month”, i.e. 5.689. Q1 and Q3 coefficients are also statistically significant. Also, the R-squared value is high at 0.8629. This means that the independent variables explain 86.29% variation in the dependent variable “Sales”. Hence, the new regression model can be expected to give accurate forecasts. Therefore, Jordan should make sure that his boss uses the seasonality forecasts because it is a more accurate predictor of sales, based on the given data.
Download Full Answer