Question

In Business and economics the studies about the factors that affect the sales are frequently undertaken, in the context and for the sake of simplicity we would like to study the effect of price ( in dollars),advertisement (in $1000), and interaction between price and advertisement on sales ($1000) of personal Care shampoo product. We selected 24 observations and we run the regression and we get the following model. Between parenthesis Student t for regression coefficient

sales= - 276+ 175*Price +19.68*Advertisement -6.0 8* (interaction between price and Advertisement)

   (-2.44) (3.93) (13.79) (-10.79)

R² =97.81%

Standard error of the estimate =28.1739

SSR=709316

SSE=15875

1. Interpret the regression coefficients
2. Test the regression coefficients at 5% level of significance
3. Forecast the sale is the Price =$2.5, Advertisement =$150000; And interaction PricexAD =2.5*1500000,
4. Compute and interpret adjusted coefficient of determination
5. Is the model valid to forecast sales of Shampoo?? Justify your answer.

Answer 1

n Business and economics the studies about the factors that affect the sales are frequently undertaken, in the context and for the sake of simplicity we would like to study the effect of price ( in dollars),advertisement (in $1000), and interaction between price and advertisement on sales ($1000) of personal Care shampoo product. We selected 24 observations and we run the regression and we get the following model. Between parenthesis Student t for regression coefficient

sales= - 276+ 175*Price +19.68*Advertisement -6.08* (interaction between price and Advertisement)

   (-2.44) (3.93) (13.79) (-10.79)

R² =97.81%

Standard error of the estimate =28.1739

SSR=709316

SSE=15875

Ans 1 ) For Price : For every one doller increase in price , there is corresponding 175 units increase in sales

For Advertisement : For every one doller spent increase in Advertisement  , there is corresponding 19.68 units increase in sales

For interaction :For every one doller increase in price and advertisement , there is corresponding 6.08 units decrease in sales

Ans 2 ) Test the regression coefficients at 5% level of significance

coefficient	standard error	t test	t crit
-276	-2.44	113.1148	significant
175	3.93	44.52926	significant
19.68	13.79	1.427121	not significant
-6.08	-10.79	0.563485	not significant

3 ) Forecast the sale is the Price =$2.5, Advertisement =$150000; And interaction PricexAD =2.5*1500000,

sales= - 276+ 175 *2.5 +19.68*150 -6.08*2.5*1500 = -19686.5

4 ) the model is valid to forecast sales of Shampoo