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,

$b_0=\frac{s_{xy}}{s_{xx}}$

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

The table can be obtained as:

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

$$\begin{gathered} \overline{y}=\frac{\sum _y}{n} \\ =5 \end{gathered}$$

$s_{xx}=10$

$s_{xy}=20$

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 data

Part (b) Step 2: Explanation   

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

Thus, the regression equation will be:$\hat{y}=1.00+2.00x$