Question

a. Find the regression equation for the data points, use the defining formulas in definition 4.4 to obtain $s_{xx}and{s}_{xy}$

b. Graph the regression equation and the data points

Short answer

(a)$\hat{y}=14-3x$

(b)

Step-by-step solution

Part(a) Step 1:Given Information   

The given data is:

We have to determine the regression equation.

Part (a) Step 2: Explanation    

The variables $b_0$and $b_1$are used to create the regression equation. For a collection of$n$ data points, the regression equation is

$\hat{y}=b_0+b_{1}x$

Where,

$b_0=\overline{y}-b_1\overline{x}$

$b_1=\frac{s_{xy}}{s_{xx}}$

The table can be obtained as:

$s_{xx}=9$

$s_{xy}=18$

Therefore,

$b_1=-0.5$

$b_0=14$

Therefore, the regression equation will be ,

$\hat{y}=14-3x$

Part (b) Step 1 :Given Information   

The given data is:

We have to determine the graph of regression equation and data points.

Part (b) Step 2: Explanation  

The regression equation and data points can be drawn on graph as: