All Flashcards
What is the correlation coefficient?
A value, r, that measures the strength and direction of a linear relationship between two variables. Ranges from -1 to 1.
Define positive correlation.
A relationship where as one variable increases, the other tends to increase.
Define negative correlation.
A relationship where as one variable increases, the other tends to decrease.
What does r = 0 indicate?
No linear correlation between the two variables.
What is a scatterplot?
A graphical representation of the relationship between two variables.
Explain the concept of correlation vs. causation.
Correlation indicates a relationship between variables, but does not prove that one variable causes the other. Other factors may be involved.
Explain the impact of outliers on the correlation coefficient, r.
The correlation coefficient, r, is not resistant to outliers. A single outlier can drastically change the value of r.
Explain the concept of linearity in correlation.
r only measures linear relationships. A strong r doesn't mean there's no relationship, just no linear one.
How do you interpret the strength of correlation based on the value of r?
Values of r closer to 1 or -1 indicate a stronger linear relationship, while values closer to 0 indicate a weaker linear relationship.
Explain how to find the correlation coefficient using a TI-84 calculator.
Enter x-values in L1 and y-values in L2. Go to STAT > CALC > LinReg(ax+b). Ensure 'DiagnosticOn' is enabled in the MODE menu to see the r value.
What are the differences between a correlation coefficient of 1 and -1?
r = 1: Perfect positive correlation (points form an exact increasing line). | r = -1: Perfect negative correlation (points form an exact decreasing line).
What are the differences between positive and negative correlation?
Positive Correlation: As one variable increases, the other tends to increase. | Negative Correlation: As one variable increases, the other tends to decrease.
What are the differences between correlation and causation?
Correlation: Measures the strength and direction of a relationship between two variables. | Causation: Indicates that one variable directly causes a change in another variable.
What are the differences between linear and non-linear relationships?
Linear Relationships: Can be accurately described by a straight line; correlation coefficient r is applicable. | Non-Linear Relationships: Cannot be accurately described by a straight line; correlation coefficient r may be misleading.
What are the differences between strong and weak correlation?
Strong Correlation: Points on a scatterplot cluster closely around a line; r is close to 1 or -1. | Weak Correlation: Points on a scatterplot are more scattered; r is closer to 0.