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Chapter 4: Q.4.5 (page 174)

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

(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,

$b_{0} = \frac{s_{x y}}{s_{x x}}$

$b_{1} = y - b_{1} x$

The table can be obtained as:

$\bar{x} = \frac{\sum_{x}}{n} = 2$

$y = \frac{\sum_{y}}{n} = 5$

$s_{x x} = 10$

$s_{x y} = 20$

Therefore,

$b_{1} = 2$

$b_{0} = 1$

Therefore, the regression equation will be

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

03

Part (b) Step 1 :Given Information

The given data is:

We have to determine the graph of regression equation and data

04

Part (b) Step 2: Explanation

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

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

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Most popular questions from this chapter

In Exercise 4.10, we give linear equations. For each equation,

a. find the $y$ -intercept and slope.

b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.

c. use two points to graph the equation.

$y = - 0.75 x - 5$

To determine whether r is positive, negative, or zero.

The $y$ intercept of a line has no effect on the steepness of the line.

The data for shell thickness and concentration of PCBs for $60$ Anacapa pelican eggs from Exercise $4.76$ are on the Weiss Stats site.

(a) Decide whether finding a regression line for the data is reasonable. If so, then also do puts $(b) - (d)$ .

Birdies and Score. The data from Exercise 4.70 for number of birdies during a tournament and final score for $63$ women golfers are on the WeissStats site.

a. decide whether use of the linear correlation coefficient as a descriptive measure for the data is appropriate, If so, then also do parts (b) and (c).

b. obtain the linear correlation coefficient.

c. interpret the value of $r$ in terms of the linear relationship between the two variables in question.

See all solutions

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