Chapter 1.7, Problem 18E

a.

To determine

To graph:

Linear model for data using regression feature and find how closely models fits to data.

Explanation of Solution

Give information:

  

Graph:

  

Interpretation:

From the graph, data is written in tabulated form as below:

$x$	$-2$	$-1$	$0$	$1$	$2$
$y$	$6$	$4$	$2$	$1$	$1$

Using regression feature of the graphing utility linear model for the above tabulated data is as above.

So, best fit linear model is $y=1.3x+2.8$

b.

To determine

To calculate:

Linear model for data numerically and find how closely models fits to data.

Answer to Problem 18E

Best fit linear model is $y=1.3x+2.8$

Explanation of Solution

Give information:

  

Calculation:

Regression line is $y=1.3x+2.8$

  $\begin{array}{l}x=-3\Rightarrow y=1.3\left(-2\right)+2.8\\ =0.2\\ x=-1\Rightarrow y=1.3\left(-1\right)+2.8\\ =1.5\\ x=0\Rightarrow y=1.3\left(0\right)+2.8\\ =2.8\\ x=1\Rightarrow y=1.3\left(1\right)+2.8\\ =4.1\\ x=4\Rightarrow y=1.3\left(2\right)+2.8\\ =5.4\end{array}$

Above values can be tabulated as below:

$x$	$-2$	$-1$	$0$	$1$	$2$
Given data	$6$	$4$	$2$	$1$	$1$
Linear equation	$0.2$	$1.5$	$2.8$	$4.1$	$5.4$

This model fits the data well.