Chapter 1.6, Problem 4CFU

a.

To determine

To graph: the given data on scatter plot.

Answer to Problem 4CFU

  

Explanation of Solution

Given information:

Year	1995	1996	1997	1998	1999	2000	2001	2002	2010
Personal consumption ($)	2294	2420	2538	2717	2927	3057	3088	3158	?

Calculation:

Let the year be x and the personal consumption be y. Plot of the graph from the given data will be as follows:

  

b.

To determine

To find: the equation of a best fit line by using two ordered pairs.

Answer to Problem 4CFU

  $y=123.43x-281150.14$

Explanation of Solution

Given information:

Year	1995	1996	1997	1998	1999	2000	2001	2002	2010
Personal consumption ($)	2294	2420	2538	2717	2927	3057	3088	3158	?

Calculation:

Select any two ordered pairs like $\left(1995,2294\right)$ and $\left(2002,3158\right)$ , and substitute the values in the slope formula as shown below.

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{3158-2294}{2002-1995}\\ =\frac{864}{7}\\ =123.43\end{array}$

Put any point coordinate and slope value into the slope intercept formula and evaluate the y -intercept as follows:

  $\begin{array}{c}y=mx+b\\ 2294=123.43\left(1995\right)+b\\ 2294=246242.85+b\\ b=2294-246242.85\\ =-243948.85\end{array}$

Now, put the values of slope and b into the slope intercept formula as follows:

  $\begin{array}{l}y=mx+b\\ y=123.43x-243948.85\end{array}$

Thus, the equation is $y=123.43x-281150.14$ .

c.

To determine

To find: the equation of regression line and its correlation value by using a graphing calculator.

Answer to Problem 4CFU

  $\begin{array}{l}y=132.79761904762x-262621.16666667\\ r=0.98448710458228\end{array}$

Explanation of Solution

Given information:

Year	1995	1996	1997	1998	1999	2000	2001	2002	2010
Personal consumption ($)	2294	2420	2538	2717	2927	3057	3088	3158	?

Calculation:

From the graph

  

By using the graphing calculator, we get slope value as $132.79761904762$ and intercept value as $-262621.16666667$ .

Now, put the values in the following equation and evaluate regression of equation of line

  $\begin{array}{l}y=mx+b\\ y=132.79761904762x-262621.16666667\end{array}$

Thus, the regression line equation is, $y=132.79761904762x-262621.16666667$ .

By using graphing calculator, the value of correlation coefficient ( r ) is $0.98448710458228$ .

d.

To determine

To explain: the whether the relationship predicted by the equation for the missing value is reliable.

Answer to Problem 4CFU

  $\approx 4302$

Explanation of Solution

Given information:

Year	1995	1996	1997	1998	1999	2000	2001	2002	2010
Personal consumption ($)	2294	2420	2538	2717	2927	3057	3088	3158	?

  $\begin{array}{l}y=132.79761904762x-262621.16666667\\ r=0.98448710458228\end{array}$

Calculation:

Since $0.75\le r\le 1$ , the equation of the regression line shows a strong relationship.

Putting the value of $x=2010$ , into the equation, we get

  $\begin{array}{c}y=132.79761904762\left(2010\right)-262621.16666667\\ =4302.047619046178\end{array}$

Irrespective of the consumer buying trends, inflation increases at a fairly steady rate. In that respect, the predicted value (i.e. 4302) is reliable though. According to the given data, the money doubles in every seven years, but it is not reflected in the data. So, there might be more variables at a play than the inflation and trends in stock market.

As the minimum wages do not increases as quickly as inflation, so the bulk of money is only with the small portion of the population. According to this, the predicted value seems reliable.