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)$\hat{y}=1-2x$

(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 regression equation is :

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

Where,

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

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

The table can be obtained as:

$$\begin{gathered} \overline{x}=\frac{\sum _x}{n} \\ =2 \end{gathered}$$

$$\begin{gathered} \overline{y}=\frac{\sum _y}{n} \\ =-3 \end{gathered}$$

$$\begin{gathered} \overline{x}=\frac{\sum _x}{n} \\ =2 \end{gathered}$$

$s_{xy}=-4$

$s_{xx}=2$

therefore,

$b_1=-2$

$b_0=1$

Therefore, the regression equation will be

$$\begin{gathered} \hat{y}=b_0+b_{1}x \\ =1-2x \end{gathered}$$

Part (b) Step 1 :Given Information 

The given data is:

We have to determine the graph of regression equation and dataponts.

Part (b) Step 2: Explanation  

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

Thus,the regression equation will be:

$\hat{y}=1.00-2.00x$