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)$\hat{y}=-3+2x$

(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 obtained by using the terms $b_{0}and{b}_1$the regression equation for a set of $n$data points 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:

$\overline{x}=2.5$

$\overline{y}=2$

$s_{xx}=5$

$s_{xy}=10$

therfore,

$b_1=2$

$b_0=-3$

therefore,the regression equation will be

$\hat{y}=-3+2x$

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:$\hat{y}=-3.00+2.00x$