   Chapter 8.4, Problem 20E ### Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640

#### Solutions

Chapter
Section ### Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640
Textbook Problem

# Online Video ADVERTISING Although still a small percentage of all online advertising, online video advertising is growing. The following table gives the projected spending on Web video advertising (in billions of dollars) through 2016: Year 2011  2012 2013 2014 2015 2016 Spending, y 2.0 3.1 4.5 6.3 7.8 9.3 a. Letting x = 0 denote 2011, find an equation of the least-squares line for these data. b. Use the result of part (a) to estimate the projected rate of growth of video advertising from 2011 through 2016. Source: eMarketer.

a.

To determine

To find: The equation of least-squares line.

Explanation

Given:

The data is as shown in below table.

 Year 2011 2012 2013 2014 2015 2016 Spending 2 3.1 4.5 6.3 7.8 9.3

Formula used:

“Suppose for n data points P1(x1,y1),P2(x2,y2),P3(x3,y3)Pn(xn,yn) .

The least-squares line for the given data is given by linear equation y=mx+b .

The normal equations are,

(x12+x22+x32++xn2)m+(x1+x2+x3++xn)b=x1y1+x2y2+x3y3++xnyn (1)

And,

(x1+x2+x3++xn)m+nb=y1+y2+y3++yn (2)

Calculation:

From the given data observe that x=0 corresponds to 20011 and the new table is calculated as shown below,

 x 0 1 2 3 4 5 y 2 3.1 4.5 6.3 7.8 9.3

That is, x1=0,x2=1,x3=2,x4=3,x5=4,x6=5 and y1=2.0, y2=3.1, y3=4.5,

y4=6.3, y5=7.8, y6=9.3 so n=6 .

Substitute the data points in normal equation (1),

[(02+12+22+32+42+52)m                  +(0+1+2+3+4+5)b]=[(0)(2.0)+(1)(3

b.

To determine

To estimate: The projected rate of growth of video advertising between 2011 and 2016 by using the result of part (a).

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