Chapter 1.1, Problem 63E

Solution

a.

To find: The scatter plot of the no of subscribers verses time and average monthly income of each subscriber verses time.

The scatter plot of the data is shown below.

  

  

Given:

The data of subscriber and number of revenue per person is shown below.

Year	No of subscribers	Average revenue per subscriber
2000	109.5	48.55
2001	128.4	49.79
2002	140.8	51
2003	158.7	51.55
2004	182.1	52.54
2005	207.9	50.65
2006	233	49.07
2007	255.4	49.26
2008	270.3	48.87
2009	285.6	47.97
2010	296.3	47.53
2011	316	46.11
2012	326.5	48.99
2013	335.7	48.79
2014	355.4	46.64
2015	377.9	44.65

Calculation:

The scatter plot of the data of subscribers’ verses time is shown below.

  

The scatter plot of the data of average monthly income verses time is shown below.

  

b.

To find: The slope intercept form of line for one of the scatter plots which is linear.

The slope intercept form of line is

Given:

The data of subscriber and number of revenue per person is shown below.

Year	No of subscribers	Average revenue per subscriber
2000	109.5	48.55
2001	128.4	49.79
2002	140.8	51
2003	158.7	51.55
2004	182.1	52.54
2005	207.9	50.65
2006	233	49.07
2007	255.4	49.26
2008	270.3	48.87
2009	285.6	47.97
2010	296.3	47.53
2011	316	46.11
2012	326.5	48.99
2013	335.7	48.79
2014	355.4	46.64
2015	377.9	44.65

The $x$ coordinate should be $x_1=0$ , $x_2=15$ , $y$ coordinate for number of subscribers, slope intercept form of the line is of the form $y=mx+b$ .

Formula used:

  $m=\frac{y_2-y_1}{x_2-x_1}$.

Calculation:

From the graphs of subscribers verses time and average monthly revenue per subscriber verses time the graph of subscribers verses time is linear.

Calculation of slope intercepts form of line for number of subscribers.

Taking $x=0$ , $x_2=15$ and $y_1=109.5$ , $y_2=377.9$

Substitute the values in the formula $m=\frac{y_2-y_1}{x_2-x_1}$.

  $\begin{array}{c}m=\frac{377.9-109.5}{15-0}\\ =17.89\end{array}$

Substitute the value of $m$ , $x_1$ , $y_1$ in the equation $y_1=m{x}_1+b$ .

  $\begin{array}{c}109.5=\left(17.89\right)\times 0+b\\ b=109.5\end{array}$

Substitute the values of $m$ and $b$ in the formula $y=mx+b$ .

  $y=17.89x+109.5$ .

c.

To find: The best fit line and scatter plot on the same graph.

The graph representing the scatter plot and the best fit line is shown below.

  

Given:

The data of subscriber and number of revenue per person is shown below.

Year	No of subscribers	Average revenue per subscriber
2000	109.5	48.55
2001	128.4	49.79
2002	140.8	51
2003	158.7	51.55
2004	182.1	52.54
2005	207.9	50.65
2006	233	49.07
2007	255.4	49.26
2008	270.3	48.87
2009	285.6	47.97
2010	296.3	47.53
2011	316	46.11
2012	326.5	48.99
2013	335.7	48.79
2014	355.4	46.64
2015	377.9	44.65

Observation:

The graph of subscriber verses time and average monthly revenue per subscriber verses time the best fit line fits appropriately to the graph of subscribers verses time.

  

d.

To find: The pattern that the graph of subscribers verses time with best fit line follow.

Some points are left after the best fit has been drawn with the help of scatter points.

Given:

The data of subscriber and number of revenue per person is shown below.

Year	No of subscribers	Average revenue per subscriber
2000	109.5	48.55
2001	128.4	49.79
2002	140.8	51
2003	158.7	51.55
2004	182.1	52.54
2005	207.9	50.65
2006	233	49.07
2007	255.4	49.26
2008	270.3	48.87
2009	285.6	47.97
2010	296.3	47.53
2011	316	46.11
2012	326.5	48.99
2013	335.7	48.79
2014	355.4	46.64
2015	377.9	44.65

Observation:

The graph of subscriber verses time with best fit line is shown below.

  

From the graph it is clear that some points are left out after drawing the best fit line with the help of scatter plot points.

e.

To find: The trend that the average monthly revenue per subscriber follows from $2005$ to $2011$ .

The decreasing and increasing pattern of revenue tells that the market the price will rose and fall according to the demand and supply.

Given:

The data of subscriber and number of revenue per person is shown below.

Year	No of subscribers	Average revenue per subscriber
2000	109.5	48.55
2001	128.4	49.79
2002	140.8	51
2003	158.7	51.55
2004	182.1	52.54
2005	207.9	50.65
2006	233	49.07
2007	255.4	49.26
2008	270.3	48.87
2009	285.6	47.97
2010	296.3	47.53
2011	316	46.11
2012	326.5	48.99
2013	335.7	48.79
2014	355.4	46.64
2015	377.9	44.65

Observation:

From the table it is clearly visible that the average monthly revenue per subscriber follows a pattern that is decreasing and after $2011$ it rose to fall again.