Question

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.884651238
R Square	0.782607814
Adjusted R Square	0.601447658
Standard Error	25.32612538
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	5	13854.44091	2770.888181	4.319977601	0.051673038
Residual	6	3848.475761	641.4126268
Total	11	17702.91667
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-53.17436031	42.95203957	-1.237993838	0.261960445	-158.274215	51.92549434	-158.274215	51.92549434
Advertising ($1000s)	2.050813091	0.763960482	2.684449181	0.036320193	0.181469133	3.92015705	0.181469133	3.92015705
t (quarters)	-4.047065728	2.779316427	-1.456137088	0.19560701	-10.84780803	2.753676575	-10.84780803	2.753676575
Q1	19.42140471	21.88478307	0.887438758	0.409003775	-34.12873036	72.97153977	-34.12873036	72.97153977
Q2	23.03418679	27.39517297	0.840811876	0.432677603	-43.99938661	90.06776019	-43.99938661	90.06776019
Q3	20.943922	25.53508827	0.820201668	0.443457241	-41.5381881	83.4260321	-41.5381881	83.4260321

1) Is there constant seasonality; increasing/decreasing seasonality; a trend; or no time effect at all from the linear regression analysis shown above? And why?

2) Are models with seasonality (Q1, Q2, Q3 included) better than models without? Why?

Answer 1

we can form the regression equation based on the coefficients as

Y = -53.17 +2.05*advertsing -4.04*t + 19.42*q1 +23.03*q2 +20.94*q3

we see that the coeffecient of q2 is higher than that of q1 and q3 , which means in q2 the sale is effected by 23.03 units , hence apparently there appears to be a seasonality , with high sales in q2

for the second part , we simply compare the r2 value of the seasonal model with the r2 value of the non seasonal model, if this value is less than 0.7826 (r2 of seasonal model) then seasonal model is better else non seasonal model would be better. However , without the data we cant run the regression