Chapter 6.5, Problem 55E

To determine

To determine whether the model is a good fit for the data by using residuals.

Answer to Problem 55E

The model is a good fit for the given data.

Explanation of Solution

Given information :

There are some data, which is given below:

x	0	1	2	3	4	5	6
y	-10	-2	-1	2	1	7	10

The equation of the line $y=3x-8$ has drawn with respect to all the points, which is give in the table.

  

There are two points $\text{F }(5,7)$ and $\text{G }(6,10)$ lie on the line.

The Slope of the line which passes through $(x_1,y_1)$ and $(x_2,y_2)$

  $\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$

Slope of the line which passes through $(-1,6)$ and $(0,1)$

  $\frac{y-7}{x-5}=\frac{10-7}{6-5}$

Now,

  $\begin{array}{l}\frac{y-7}{x-5}=\frac{10-7}{6-5}\\ \frac{y-7}{x-5}=\frac{3}{1}\\ y-7=3(x-5)\\ y-7=3x-15\\ y=3x-8\end{array}$

Therefore,

The derived equation of the line is similar to the give given equation.

Hence,

The model is a good fit for the given data.