Final answer:
A regression analysis determines the degree of association between variables. The process involves identifying independent and dependent variables, creating a scatter plot, fitting a regression line, calculating and interpreting the correlation coefficient, and assessing the linearity of the relationship.
Step-by-step explanation:
A regression analysis is used to determine the degree of association between variables. This means it helps to identify how strongly two variables are related and in what way. For example, in a study about the effects of fast food outlets on obesity rates, independent variables might include the number of fast food joints, ethnicity, income, and access to parks, while the dependent variable would be obesity.
When conducting a regression analysis, steps typically involve:
- Deciding which variables are independent and which is the dependent variable.
- Drawing a scatter plot to visually assess the potential relationship between the variables.
- Using regression techniques to find the line of best fit, often expressed in the form ΓΏ = a + bx, where a is the y-intercept and b is the slope of the line.
- Finding the correlation coefficient, which quantifies the degree of association.
- Interpreting the significance of the correlation coefficient to judge the reliability of the association.
- Evaluating whether there is a linear relationship between the variables based on the line of best fit and the value of the correlation coefficient.
These steps help to build a model that predicts the dependent variable based on the values of the independent variables and to assess the strength and significance of the relationship between them.