Question

Consider the following sample data for the relationship between advertising budget and sales for Product A: Observation 1 2 3 4 5 6 7 8 9 10 Advertising ($) 40,000 50,000 50,000 60,000 70,000 70,000 80,000 80,000 90,000 100,000 Sales ($) 240,000 308,000 315,000 358,000 425,000 440,000 499,000 494,000 536,000 604,000 What is the slope of the "least-squares" best-fit regression line? Please round your answer to the nearest hundredth. Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel.

Answer 1

Line of Regression Y on X i.e Y = bo + b1 X
					X	Y	(Xi - Mean)^2	(Yi - Mean)^2	(Xi-Mean)*(Yi-Mean)
40000	240000	841000000	33087610000	5275100000
50000	308000	361000000	12973210000	2164100000
50000	315000	361000000	11427610000	2031100000
60000	358000	81000000	4083210000	575100000
70000	425000	1000000	9610000	3100000
70000	440000	1000000	327610000	18100000
80000	499000	121000000	5944410000	848100000
80000	494000	121000000	5198410000	793100000
90000	536000	441000000	13018810000	2396100000
100000	604000	961000000	33160410000	5645100000

calculation procedure for regression
mean of X = sum ( X / n ) = 69000
mean of Y = sum ( Y / n ) = 421900
sum ( (Xi - Mean)^2 ) = 3290000000
sum ( (Yi - Mean)^2 ) = 119230900000
sum ( (Xi-Mean)*(Yi-Mean) ) = 19749000000
b1 = sum ( (Xi-Mean)*(Yi-Mean) ) / sum ( (Xi - Mean)^2 )
= 19749000000 / 3290000000
= 6.0027
bo = sum ( Y / n ) - b1 * sum ( X / n )
bo = 421900 - 6.0027*69000 = 7711.2462
value of regression equation is, Y = bo + b1 X
Y'=7711.2462+6.0027* X          

slope of the equation is 6.0027,
the above equation compare with y = m*x +c here, m is the slope of the equation