Final answer:
The correlation coefficient measures the strength of the linear association between two variables. It ranges from -1 to 1. A positive value indicates a positive relationship, while a negative value indicates an inverse relationship.
Step-by-step explanation:
Definition:
The correlation coefficient, r, measures the strength of the linear association between two variables, x and y. It is represented by a numerical value between -1 and 1. A positive value indicates that x and y tend to increase or decrease together, while a negative value indicates an inverse relationship.
a. Definition of variables:
The independent variable, x, is the variable that is manipulated or controlled in an experiment. The dependent variable, y, is the variable that is measured or observed in response to changes in the independent variable.
b. Scatter plot:
A scatter plot is a graph that shows the relationship between two variables. The independent variable, x, is plotted on the horizontal axis, and the dependent variable, y, is plotted on the vertical axis. Each data point is represented by a dot on the graph.
c. Regression analysis:
Regression analysis is used to find the line of best fit for the data points on a scatter plot. This line represents the relationship between the independent and dependent variables. The correlation coefficient, r, can be calculated using regression analysis.
d. Interpretation of correlation coefficient:
The correlation coefficient, r, tells us about the strength and direction of the relationship between the variables. A value close to 1 or -1 indicates a strong relationship, while a value close to 0 indicates a weak relationship. The coefficient of determination, r², represents the percentage of variation in the dependent variable that can be explained by the independent variable.
e. Linear relationship:
The correlation coefficient, r, measures the strength of the linear relationship between the variables. If the correlation coefficient is close to 1 or -1, it indicates a strong linear relationship. If it is close to 0, it indicates a weak or no linear relationship.