Question

Judge and Cable (2010) demonstrated a positive relationship between weight and income for a group of men. The following are data similar to those obtained in the study. To simplify the weight variable, the men are classified into five categories that measure actual weight relative to height, from 1 5 thinnest to 5 5 heaviest. Income is recorded as thousands earned annually

4 151
5 88

3 52

2 73

1 49

3 92

1 56

5 143Calculate the Pearson correlation for these data.

Answer 1

The Pearson correlation coefficient measures the strength and direction of a linear relationship between weight and income. To calculate it, find the mean and standard deviation of the weight and income data, calculate the deviation of each observation from their means, multiply the deviations, add them up, and divide by the product of the standard deviations.

Step-by-step explanation:

The Pearson correlation coefficient measures the strength and direction of a linear relationship between two variables. To calculate the Pearson correlation coefficient for the given data, you can use a statistical software or spreadsheet program. Here are the steps to calculate it:

1. Find the mean and standard deviation of the weight and income data.
2. Calculate the deviation of each weight and income observation from their respective means.
3. Multiply the deviations of weight and income for each observation.
4. Add up all the multiplied deviations.
5. Divide the sum by the product of the standard deviations of weight and income.

The resulting value is the Pearson correlation coefficient, which ranges from -1 to 1. A positive value indicates a positive correlation, meaning that as weight increases, income also tends to increase.