Chapter ISG, Problem 4.4.1P

To determine

To find: The equation of line of fit of the given scatters plots.

Answer to Problem 4.4.1P

The left side scatter plot shows the negative correlation and the right side scatter plot shows the positive correlation and the equation of line of fit of the scatters plots are given below.

Explanation of Solution

Given information: The data given scatter plots are:

  

Calculation:

The left side scatter plot shows the negative correlation and the right side scatter plot shows the positive correlation.

The equation of the line is given as:

  $y-y_1=m\left(x-x_1\right)$

The line of fit that shows the trend of the given data of the left scatter plot is as:

  

As the above scatter plot shows the line passes through the points $\left(28,28\right)\&\left(44,12\right)$ , so the equation of the above fit is line is given as:

  $\begin{array}{c}\left(y-12\right)=\frac{16}{-16}\left(x-44\right)\\ \left(y-10\right)=-1\left(x-44\right)\\ y-10=-x+44\\ x+y=54\end{array}$

And the line of fit that shows the trend of the given data of the right scatter plot is as:

  

As the above scatter plot shows the line passes through the points $\left(5,5\right)\&\left(10,12\right)$ , so the equation of the above fit is line is given as:

  $\begin{array}{c}\left(y-12\right)=\frac{5-12}{5-10}\left(x-10\right)\\ \left(y-12\right)=\frac{7}{5}\left(x-10\right)\\ 5y-60=7x-50\\ 7x-5y=10\end{array}$

Therefore, the equation of line of fit of the given two scatter plot are given above.