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Chapter 4: Q.4.49 (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,

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

$b_{0} = y - b_{1} x$

The table can be obtained as:

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

$y = \frac{\sum_{y}}{n} = - 3$

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

$s_{x y} = - 4$

$s_{x x} = 2$

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 dataponts.

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

For a data set consisting of two data points:

a. identify the regression line.

b. What is the sum of squared errors for the regression line? Explain your answer.

For which of the following sets of data points can you reasonably determine a regression line? Explain your answer.

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 $(b) - (d)$ .

The data for gas mileage and engine displacement for $121$ vehicles from Exercise $4.78$ are provided on the Weiss Stats site.

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

The linear correlation coefficient of a set of data points is $(), ․ 16$ .

a. Is the slope of the regression line positive or negative? Explain your answers.

b. Determine the coefficient of determination.

See all solutions

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