Question

Calculate the correlation coefficient for the number of years out of school and annual contribution data (in thousands of dollars).

A) Use the mean formula
B) Use the median formula
C) Apply the Pearson correlation formula
D) Apply the standard deviation formula

Answer 1

The Pearson correlation formula assesses the linear relationship between the number of years out of school and annual contribution data, providing a standardized measure of their correlation. Thus the option c is correct C) Apply the Pearson correlation formula

Step-by-step explanation:

In calculating the correlation coefficient for the number of years out of school and annual contribution data, the appropriate method is to apply the Pearson correlation formula (Option C).

This method assesses the linear relationship between two variables, providing a standardized measure of how much they change together. To calculate the Pearson correlation coefficient, the formula involves dividing the covariance of the two variables by the product of their standard deviations.

To elaborate, let X represent the number of years out of school,
`\(Y\)`represent annual contribution data,
`\(\bar{X}\)` denote the mean of X,
`\(\bar{Y}\)`denote the mean of
`\(Y\), \(s_X\)` denote the standard deviation of X, and
`\(s_Y\)`denote the standard deviation of Y. The Pearson correlation coefficient
`(\(r\))` is given by the formula:

`\[ r = \frac{\sum{(X_i - \bar{X})(Y_i - \bar{Y})}}{\sqrt{\sum{(X_i - \bar{X})^2} \cdot \sum{(Y_i - \bar{Y})^2}}} \]`

After obtaining the values of r, it can be interpreted as follows: r = 1 indicates a perfect positive linear relationship, r = -1 indicates a perfect negative linear relationship, and r = 0 indicates no linear relationship.