Question

Q3. A company in the field of fast moving consumer goods has launched several new products in recent years. The sales manager has to provide a forecast for sales in the next quarter. These forecasts are used to draw up an initial production plan, which is updated daily as new data becomes available. To provide these forecasts, the sales manager has conducted regression analysis but needs your advice on its interpretation. Extracts from the Excel regression analysis for products A and B, conducted using data on the number of units sold in each of the past 24 months, are shown on pages 5-7. Note - in the data set the code 1-24 has been used to denote month 1-24 respectively. Use this output to answer the questions below. (a) Based on the scatter plots shown in Figures Q3a-b only, comment upon the patterns in sales for products A and B. (4 marks) (b) Write down the regression models for each of products A and B. Interpret these models in terms the sales manager will understand. What would be your best forecast for month 25 for each of products A and B? (7 marks) (c) Explain whether the parameters of these two regression models are statistically significant by using and interpreting appropriate confidence intervals. (5 marks)

Answer 1

a) Based on the given scatter plots we have to comment on the patterns of sales for A and B. For product A we see there is a positive association between months and units sold i.e, the monthly sales increases gradually.

For product B we see there is a negative association between months and units sold i.e, the monthly sales decreases gradually.

b) Here we have to write the regression equation and forecast the value of month 25 for both the values A and B .

Product A:

The regression equation is : Sales= 14898.19 + 138.48 Month.

Forecast for month 25 is:   Sales= 14898.19+ 138.48* 25= 18360.19

Product B:

The regression equation is : Sales= 10139.86 + 2.48 Month.

Forecast for month 25 is:   Sales= 10139.86+ 2.48* 25= 10201.86

c) Here we have to interprete the parameters of the 2 regression models

We know if the true value of the coefficient i.e, 0 lies within the confidence interval then it is not significant.

For product A the confidence interval of intercept is (14196.72, 15599.65) and for month is (89.39,187.57) . Thus here we see both the parameters donot contain 0 within the confidence intervals so both of them are significant.

For product B the confidence interval of intercept is (8612.39,11667.32) and for month is (-104.42,109.38) . Here we see that for intercept there is no 0 in the confidence interval so it is significant while for month there is 0 in the confidence interval so it is not significant.

d) Here we have to interprete the R square and the residual plots for both the products.

Product A:

The r square value = 0.6087 . Thus we can say that 60.87% of the total variance is explained. From the residual plot we see a random pattern which suggests a moderately good fit.

Product B:

The r square value = 0.0001 . Thus we can say that 0.01% of the total variance is explained. From the residual plot we see no random pattern which suggests it is not a good fit.