5. The table below shows Psychology exam scores, Statistics Exam scores, and IQ scores for a random sample of students. What can you observe in the relationship between IQ and psychology, psychology and statistics, and IQ and statistics? Using a web-calculator, obtain the Pearson’s r and coefficient of determination for the following relationships.
b.Between the IQ and statistics scores
c.Between the psychology scores and statistics scores.
Student number IQ Psychology Statistics
101 142 49 49
102 100 30 32
103 103 36 38
104 121 44 41
105 120 35 42
106 115 47 43
Do you have a web-calculator?
To observe the relationship between variables and obtain the Pearson’s r and coefficient of determination, you can follow these steps:
1. Calculate the Pearson’s correlation coefficient (r) using an online calculator or statistical software.
a. For the relationship between IQ and statistics scores, you need to extract the IQ scores and statistics scores from the table.
- IQ scores: 142, 100, 103, 121, 120, 115
- Statistics scores: 49, 32, 38, 41, 42, 43
Plug these values into a Pearson's correlation coefficient calculator to obtain the value of r. The Pearson's r ranges from -1 to +1, with values close to +1 indicating a strong positive correlation, values close to -1 indicating a strong negative correlation, and values close to 0 indicating little to no correlation.
b. For the relationship between psychology scores and statistics scores, you need to extract the psychology scores and statistics scores from the table.
- Psychology scores: 49, 30, 36, 44, 35, 47
- Statistics scores: 49, 32, 38, 41, 42, 43
Plug these values into a Pearson's correlation coefficient calculator to obtain the value of r.
2. Once you have obtained the value of r for each relationship, you can also calculate the coefficient of determination (r^2). The coefficient of determination represents the proportion of variance in the dependent variable that can be predicted from the independent variable(s). It ranges from 0 to 1, with higher values indicating a stronger relationship between the variables. Simply square the value of r to obtain r^2.
By following these steps and using an online calculator or statistical software, you can obtain the Pearson’s r and coefficient of determination for the relationships between IQ and statistics scores, as well as psychology scores and statistics scores.