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Chapter 4: Q.4.48 (page 173)

a. Find the regression equation for the data points, use the defining formulas in definition 4.4 to obtain $s_{x x} a n d s_{x y}$
b. Graph the regression equation and the data points

Short Answer

Expert verified

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

(b)

Step by step solution

01

Part(a) Step 1:Given Information

The given data is:

We have to determine the regression equation.

02

Part (a) Step 2: Explanation

The regression equation is:

$\hat{y} = b_{0} + b_{1} x$

where,

$b_{1} = \frac{s_{x y}}{s_{x x}}$

$b_{0} = \overset{炉}{y} - b_{1} x$

The table can be obtained as:

$\overset{炉}{x} = \frac{\underset{x}{鈭�}}{n} = 3$

$y = \frac{\underset{y}{鈭�}}{n} = 5$

$s_{x x} = \underset{x i^{2}}{鈭�} - \frac{{(\underset{x_{i}}{鈭�})}^{2}}{n} = 2$

$s_{x y} = \underset{x i y i}{鈭�} - \frac{(\underset{x i}{鈭�}) (\underset{y i}{鈭�})}{n} = 2$

therefore,

$b_{1} = 1$

$b_{0} = 2$

therefore,the regression equation will be

$\hat{y} = b_{0} + b_{1} x = 2 + x$

03

Part (b) Step 1 :Given Information

The given data is:

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

04

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:

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

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