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)$\hat{y}=2+x$

(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:

$$\begin{gathered} \overline{x}=\frac{\sum _x}{n} \\ =3 \end{gathered}$$

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

$$\begin{gathered} s_{xx}=\sum _{x{i}^2}-\frac{{\left(\sum _{x_i}\right)}^2}{n} \\ =2 \end{gathered}$$

$$\begin{gathered} s_{xy}=\sum _{xiyi}-\frac{\left(\sum _{xi}\right)\left(\sum _{yi}\right)}{n} \\ =2 \end{gathered}$$

therefore,

$b_1=1$

$b_0=2$

therefore,the regression equation will be

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

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 

On a graph, the regression equation and data points can be represented as follows:

Thus, the regression equation will be:

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