Question

Multiple Regression Analysis The company has been able to determine that its sales in dollars depend on advertising and of the number of sellers and for this reason, it uses the data from previous years to be able to forecast possible sales for the year 2020. Y X1 ($ 000) X2 ($ 000) Year S ales Advertising Salesman 2013 $ 10 $1 2014 $15 $ 2 2015 $25 $3 2016 $ 40 $5 2017 $ 70 $6 2018 $ 110 $8 2019 $ 150 $9 INSTRUCTIONS: a) Calculate the values of the letters a b1,b2. (excel) b) Write down the problem Regression equation c) Calculate sales by 2020 if the advertising were $ 14,000 and the number of sellers out of 10 ates) | o = 0. stage 2

Answer 1

The following data is given in problem. We want to predict the Sales (S) based on Advertising (A) and Salesman (Sa).

Year	Sales (S)	Advertising (A)	Salesman (Sa)
2013	10	1	1
2014	15	2	1
2015	25	3	2
2016	40	5	3
2017	70	6	3
2018	110	8	4
2019	150	9	6

a) The regression equation is S = a +b1*A+ b2 * Sa +u

Running the regression in excel we get the following result.

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-23.96	11.11	-2.16	0.10	-54.80	6.89	-54.80	6.89
Advertising (A)	7.60	6.96	1.09	0.34	-11.73	26.94	-11.73	26.94
Salesmane (Sa)	16.46	11.88	1.39	0.24	-16.52	49.43	-16.52	49.43

Thus, a = -23.96

b1 = 7.60

b2 = 16.46

b) The regression equation is - S = -23.96 + 7.60A + 16.46Sa

c) In 2020, A = 14 and Sa = 10

Putting these values in the above equation we get,

Y = -23.96 + 7.60 * 14 + 16.46 * 10 = 247

Thus, sales in 2020 = 247000