Final answer:
Regression analysis measures the relationship between a dependent variable (Y) and an independent variable (X), used to find the line of best fit and the correlation coefficient which indicate the relationship's strength and direction.
Step-by-step explanation:
A regression analysis measures the strength of the relationship between a dependent variable (Y) and an independent variable (X). Regression analysis can be used to find the line of best fit and the correlation coefficient, which indicates the degree and direction of the relationship between the variables.
- Independent and dependent variables are chosen based on the context of the study, where the independent variable (X) is the cause or predictor, and the dependent variable (Y) is the effect or outcome that is being measured.
- To visualize the relationship between the two variables, you draw a scatter plot with the independent variable on the horizontal axis and the dependent variable on the vertical axis.
- Inspecting the scatter plot can give a preliminary idea of whether there is a relationship between the variables.
- Using regression, you can calculate the least-squares line, which is represented by the equation ý = a + bx, where 'a' is the y-intercept and 'b' is the slope of the line.
- The correlation coefficient, usually denoted as 'r', is calculated to quantify the strength and direction of the linear relationship between two variables. A value of 'r' close to 1 or -1 indicates a strong positive or negative linear relationship, whereas a value close to 0 indicates no linear relationship.
- The significance of 'r' determines whether the linear relationship is likely to be due to chance. A significant correlation implies that the relationship observed in the sample data is likely to exist in the population from which the sample was taken.
- The linearity of the variables is assessed to determine if a linear model is appropriate for the data. Other types of relationships may require different models.