Chapter 1.7, Problem 23E

(a)

To determine

To graph: the data given in the table.

Explanation of Solution

Given data:

Table of year v/s Population

Formula used:

Slope intercept form:

  $\begin{array}{l}y=mx+C\\ m=\frac{y_2-y_1}{x_2-x_1}\end{array}$

Calculation:

Graph for the given table:

Year	Population, P (in millions)
2013	1.867
2014	1.881
2015	1.894
2016	1.908
2017	1.920

  

Interpretation:

Population increases with year.

(b)

To determine

To find: Linear regression of model

Answer to Problem 23E

Linear regression of model is $y=0.01x+1.7$

Explanation of Solution

Given data:

Table of year v/s Population.

Formula used:

Slope intercept form:

  $\begin{array}{l}y=mx+C\\ m=\frac{y_2-y_1}{x_2-x_1}\end{array}$

Calculation:

Linear regression of the model:

  $\begin{array}{l}y=mx+C\\ m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{1.92-1.867}{2017-2013}\\ m=\frac{0.05}{4}\\ m=0.01\\ C=1.7\\ \\ y=0.01x+1.7\end{array}$

Conclusion:

Linear regression of model is $y=0.01x+1.7$

(c)

To determine

To find: If linear model is a good fit.

Answer to Problem 23E

Yes it is a good fit.

Explanation of Solution

Given data:

Table of year v/s Population.

Formula used:

Slope intercept form:

  $\begin{array}{l}y=mx+C\\ m=\frac{y_2-y_1}{x_2-x_1}\end{array}$

Calculation:

Yes this is a good fit because line of fit is have value nearly to original values.

  

Conclusion:

Yes it is a good fit.

(c)

To determine

To graph: Linear model and original graph in same window.

Explanation of Solution

Given data:

Table of year v/s Population.

Formula used:

Slope intercept form:

  $\begin{array}{l}y=mx+C\\ m=\frac{y_2-y_1}{x_2-x_1}\end{array}$

Calculation:

  

(d)

To determine

To find: Table of linear model value and original value.

Answer to Problem 23E

The values are differ by 0.043

Explanation of Solution

Given data:

Table of year v/s Population.

Calculation:

Table of original value and model equation value :

Year	Original values	Model values
2013	1.867	1.824
2014	1.881	1.834
2015	1.894	1.844
2016	1.908	1.859
2017	1.920	1.864

These values are differ by 0.043.

Conclusion:

The values are differ by 0.043

(e)

To determine

Population in 2021.

Answer to Problem 23E

Population in 2021 will be 1.92 millions.

Explanation of Solution

Given data:

Table of year v/s Population.

Calculation:

Population in 2021 will be:

  $\begin{array}{l}y=0.01x+1.7\\ y=0.01(21)+1.7\\ y=1.91\text{millions}\end{array}$

It is not reasonable answer because as the graph is increasing with year and population also increases.

Conclusion:

Population in 2021 will be 1.92 millions.