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 ($)	90,000	100,000	100,000	110,000	120,000	120,000	130,000	140,000	140,000	150,000
Sales ($)	535,000	626,000	625,000	674,000	712,000	725,000	809,000	832,000	845,000	919,000

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

Solution:

	x	y	x^2	xy
	90000	535	8100000000	48150000
	100	626	10000	62600
	100	625	10000	62500
	110	674	12100	74140
	120	712	14400	85440
	120	725	14400	87000
	130	809	16900	105170
	140	832	19600	116480
	140	845	19600	118300
	150000	919000	2.25E+10	1.38E+11
SUM	240960	925383	3.06E+10	1.38E+11

nn = 10,

240960

Σx =

925383

Σy =

  

x *y = 1.38 * 1011

2 Σ = 3.06 * 1010

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let a linear model

                                                                                                                                            (1)

y=potßix

                    

Σy = βο Σ1 +β, Σx

                                                                                                                        (2)                                                                                                                   

925383 - 10B. +24096031

Multiplying by x in eqn. (1) and taking sum both side

Σxy = βοΣ +β, Σx?

                                                                                                                      (3)

1.38 * 1011 = 240960B. +3.06 * 1010B1

Solving eqn. (2) , (3)

Bo = -1.9907 * 104 = -19907

B. = 4.6666

linear model is

y == -19907 + 4.6666x

So slope is β1=4.6666

B. = 4.6666