1 answer

Consider the following sample data for the relationship between advertising budget and sales for Product A:...

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 ($) 70,000 80,000 80,000 90,000 100,000 100,000 110,000 110,000 120,000 130,000
Sales ($) 432,000 478,000 484,000 552,000 605,000 594,000 688,000 674,000 713,000 784,000

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.


Answers

We would make each of the values in 1000 dollars, so as to make the calculation easier.

Let X be the advertising budget and Y be the sales.

The least-square best-fit regression line will be of the form

Y = a + bX

From the given data, we have

\bg_white \sum x = 990 \sum xy = 614080 \sum x^2 = 101300 \sum y = 6004

The normal equations required to find the regression line are given by

\sum y = na + b\sum x

6004 = 10a + 990b ----------------------(i)

and

\bg_white \sum xy = a \sum x + b\sum x^2

\bg_white 614080 = 990a + 614080b ---------------(ii)

Solving these two simultaneous equations, we have

a = 8.0851

b = 5.983

The regression line is

y = 5.983x + 8.0851

The slope of the least-square best-fit regression line is = 5.98

Thank You!! Please Upvote!!

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