1) Is there constant seasonality; increasing/decreasing seasonality; a trend; or

Question

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?

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

Explanation / Answer

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

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