Final answer:
Correlation coefficients represent the strength and direction of the relationship between two variables, ranging from -1 (perfect negative correlation) to +1 (perfect positive correlation), with 0 indicating no correlation. The given statements pertain to negative correlation, no correlation, and positive correlation, allowing us to match the variables with their most likely correlations accordingly.
Step-by-step explanation:
Correlation is a statistical measure that describes the strength and direction of a relationship between two variables. The correlation coefficient, often represented by the letter r, ranges from -1 to +1. A value of +1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and a value of 0 indicates no correlation. The statements provided correspond to the following correlation coefficient descriptions:
- Goes down from left to right in a line: This describes a negative correlation, where an increase in one variable is associated with a decrease in another.
- Points do not form a line: This indicates that there is no correlation or a very weak correlation between the variables.
- Goes up from left to right in a line: This indicates a positive correlation, meaning as one variable increases, the other variable also increases.
The most likely correlation for the variables provided would be:
- Number of minutes working out, calories burned: Positive Correlation.
- Number of credit hours earned, time until graduation: Negative Correlation.
- Stars in the sky, number of points scored in a football game: No Correlation.
It's essential to remember that correlation does not imply causation, and other statistical methods should be considered if the data doesn't seem to fit a linear model.