Chapter 14, Problem 1P

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?

To determine

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

Answer to Problem 1P

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 of Solution

Justification:

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

$r=\frac{SP}{\sqrt{S{S}_{X}S{S}_Y}}$

Where the co-variability of the variable X and Y  is $SP$, $S{S}_X$ is the variability of the x variable and $S{S}_Y$ 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.

To determine

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

Answer to Problem 1P

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 of Solution

Justification:

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

$r=\frac{SP}{\sqrt{S{S}_{X}S{S}_Y}}$

Where the co variability of the variable x and y is $SP$, $S{S}_X$ is the variability of the x variable and $S{S}_Y$ 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.