   Chapter 14, Problem 1P Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

Solutions

Chapter
Section Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

a. What information is provided by the sign (+ or −) of the Pearson correlation?b. What information is provided by the numerical value of the Pearson correlation?

a.

To determine

To explain: The information provided by sign of Pearson correlation.

The positive correlation indicates that the both variables are increase or decrease in same direction and negative correlation indicates that the both variables are changing in opposite directions.

Explanation

Justification:

The Pearson correlation coefficient is defined as ratio of co-variability of the variables with the variability of both variables.

r=SPSSXSSY

Where the co-variability of the variable X and Y  is SP, SSX is the variability of the x variable and SSY is the variability of the y variable.

Pearson correlation sign shows the nature of the correlation between two or more variables.

Positive sign shows that the correlation is positive and negative sign shows the negative correlation between the variables, if the Pearson correlation is 0 that means there are no correlations between the variables.

The positive correlation indicates that the both variables are increase or decrease in same direction and negative correlation indicates that the both variables are changing in opposite directions.

b.

To determine

To explain: The information provided by numerical value of the Pearson correlation.

If the value is 1 or –1 it indicating that the perfect linear relationship between the variables and the value 0 indicating that they are not linearly related.

Explanation

Justification:

The Pearson correlation coefficient is defined as ratio of co variability of the variables with the variability of both variables.

r=SPSSXSSY

Where the co variability of the variable x and y is SP, SSX is the variability of the x variable and SSY is the variability of the y variable.

Numerical value of the Pearson correlation shows the strong and weak nature of the correlation between the variable.

If the value is 1 or –1 it indicating that the perfect linear relationship between the variables and the value 0 indicating that they are not linearly related.

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