Question

The following data relate to the sales of a product over an 8-month period:

MONTH	Jan	Feb	Mar	Apr	May	June	July	Aug
Sales (units)	56	72	70	65	68	75	66	67
Price ($)	75	65	59	69	69	49	59	59

a) Investigate whether sales are affected more by the level of price or by the change in price of the product.

b) Interpret the regression coefficient of the explanatory variable.

c) Forecast sales in September if price is $65.

Answer 1

a)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.7695
R Square	0.5921
Adjusted R Square	0.5241
Standard Error	3.9014
Observations	8.0
ANOVA
	df	SS	MS	F	Significance F
Regression	1	132.5517	132.5517	8.7087	0.0256
Residual	6	91.3233	15.2205
Total	7	223.8750
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	101.05	11.4934	8.7918	0.0001	72.9242	129.1706
Price ($)	-0.5345	0.1811	-2.9511	0.0256	-0.9777	-0.0913

Change in price has significant affect on sales as the P-value of price coefficient is significant at 5% level

b) The value of regression coefficient is -0.5345 which means for one unit increase in price the sales decreases by 0.54 units

c) Forecast sales in September = 101.05-0.54*65 = 66 units