Chapter 4: Q. 4.143 (page 189)

Determine the linear correlation coefficient by using
a. definition 4.8 on page 183.
b. Formula 4.3 on page 185.
Compare your answers in parts (a) and (b).

Short Answer

Expert verified

The linear correlation coefficient of the given set of data is, $- 0.685$ .

Step by step solution

Step 1. Given information

Step 2. Table for obtaining the linear correlation coefficient is,

$x$	$y$	$x y$	$x^{2}$	$y^{2}$
$0$	$4$	$0$	$0$	$16$
$2$	$2$	$4$	$4$	$4$
$2$	$0$	$0$	$4$	$0$
$5$	$- 2$	$- 10$	$25$	$4$
$6$	$1$	$6$	$36$	$1$
$\sum x = 15$	$\sum y = 5$	$\sum x y = 0$	$\sum x^{2} = 69$	$\sum y^{2} = 25$

Step 3. The linear correlation coefficient of given set of data is,

$r = \frac{\sum x_{i} y_{i} - \frac{(\sum x_{i}) (\sum y_{i})}{n}}{\sqrt{[\sum x_{i}^{2} - \frac{{(\sum x_{i})}^{2}}{n}] [\sum y_{i}^{2} - \frac{{(\sum y_{i})}^{2}}{n}]}} = \frac{0 - \frac{(15) (5)}{5}}{\sqrt{[69 - \frac{{(15)}^{2}}{5}] [25 - \frac{{(5)}^{2}}{5}]}} = - 0.685$

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Determine the linear correlation coefficient by using
a. definition 4.8 on page 183.
b. Formula 4.3 on page 185.
Compare your answers in parts (a) and (b).

Short Answer

Step by step solution

Step 1. Given information

Step 2. Table for obtaining the linear correlation coefficient is,

Step 3. The linear correlation coefficient of given set of data is,

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Determine the linear correlation coefficient by usinga. definition 4.8 on page 183.b. Formula 4.3 on page 185.Compare your answers in parts (a) and (b).

Short Answer

Step by step solution

Step 1. Given information

Step 2. Table for obtaining the linear correlation coefficient is,

Step 3. The linear correlation coefficient of given set of data is,

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Geometry

Applied Mathematics

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Determine the linear correlation coefficient by using
a. definition 4.8 on page 183.
b. Formula 4.3 on page 185.
Compare your answers in parts (a) and (b).