Correlation evaluates the direction and strength of the linear relationship between two variables (X and Y) and produces a correlation coefficient: r. The square of the correlation coefficient, r*, is called the coefficient of determination and is a measure of how much of the variation of one variable (Y) is explained by the variation in the other variable (X). Regression plots a “line of best fit” for the relationship between two variables. Regression identifies one of the variables as a dependent (Y) on one or more independent variables (X1, X2, X3. Etc.). Each independent variable (X) will have a corresponding coefficient or slope (B). The remaining variation in the dependent variable is accounted for by intercept (a). Using the regression formula {Y=bXi+a) a prediction about the average value of Y for any value of X can be made.
Correlation and Regression Research Instructions
For your research note, you will need to select one continuous, interval/ratio variable to be your dependent variable (Y) and a minimum of three independent variables (X). You will need at least one continuous interval/ratio independent variable and one dichotomous independent variable. First, you will run a correlation for each variable (corr Y x1 x2 x3). Next, you will run a simple regression for each independent variable on the dependent variable (reg Y X1; reg Y X3; reg Y x3). Finally, you will run a multiple regression with all the independent variables (reg Y x1 x2 x3).
Your regression research note will consist of three parts:
1) An essay interpreting the results of Your correlations and regressions,
2) two tables on containing your correlation coefficients and containing the results of your simple and multiple regressions, and
3) a scatter plot with the relationship between your two continuous variables.
Your essay should contain the following components. 1) A research question centered on your dependent variable, 2) an interpretation of your correlation coefficients for each independent variable and your dependent variable, 3) an interpretation of each simple regression coefficient, 4) an interpretation of each regression coefficient in your multiple regression and the intercept (cons) and an interpretation of Your regression table needs to include the independent variables, a column for each model: the regression coefficient and standard error in parentheses below, and on the indicator of significance, and r2 (see examples below). Your scatter plot should contain both continuous variables you are using.
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