How to (1)Comment on the R-squared.
(2). Conduct the test of significance for the regression equation in part 1. Interpret your finding.
(3). Interpret the correlation coefficient.
(4). Test the significance of the strength of relationship. ( use á =.10)
Data
School-Enroll-Per Faculty-Tuition-Foreign Tuition-Age-%Foreign-Start Salary
A---200--5--24420--29,600--28--47--71400
B---228--4--19993--32,582--29--28--65200
C---392--5--4300--4300--22--0--7100
D---90--5--11140--11140--29--10--31000
E---126--4--33060--33060--28--60--87000
For correlation, r^2 is a measure of effect size. It's the correlation coefficient squared and basically represents the proportion of variability that is shared by two variables. The r^2 value may show this effect to be strong or weak.
As an example, suppose we have r^2 = .44; this means the proportion of variability shared by two variables represents a strong effect.
I hope this will help.
To comment on the R-squared, conduct the test of significance for the regression equation, interpret the correlation coefficient, and test the significance of the strength of relationship, you will first need to perform a regression analysis using a statistical software package such as Excel, SPSS, or R.
Here are the steps to follow:
1. Open your chosen statistical software package.
2. Enter the provided data (School, Enroll, Per Faculty, Tuition, Foreign Tuition, Age, %Foreign, Start Salary) into the software.
3. Run a regression analysis with "Start Salary" as the dependent variable and the other variables (Enroll, Per Faculty, Tuition, Foreign Tuition, Age, %Foreign) as independent variables. The specific steps to perform this analysis will depend on the software you are using, but it typically involves selecting the variables and running a regression model or using a regression function.
4. Once the regression analysis is complete, you can obtain various statistics, including the R-squared, significance tests, and correlation coefficients.
To comment on the R-squared:
- R-squared is a measure of how well the independent variables explain the variation in the dependent variable. It ranges from 0 to 1, where 0 represents no variation explained, and 1 represents all the variation explained.
- A higher R-squared indicates a better fit of the regression model. If R-squared is close to 1, it means the independent variables are good predictors of the dependent variable.
- However, R-squared alone should not be used to determine the goodness of fit. It is essential to consider other statistical measures, examine the assumptions of the regression model, and interpret the coefficient estimates to make accurate conclusions.
To conduct a test of significance for the regression equation:
- Look for the p-value associated with the overall regression model (also known as the F-test).
- The p-value measures the probability of observing the results (or more extreme results) if the null hypothesis is true.
- If the p-value is less than your chosen significance level (alpha), typically 0.05 or 0.10, you can reject the null hypothesis and conclude that the regression equation is significant.
- If the p-value is greater than the significance level, you fail to reject the null hypothesis and interpret that the regression equation is not statistically significant.
To interpret the correlation coefficient:
- The correlation coefficient measures the strength and direction of the linear relationship between two variables, in this case, "Start Salary" and the independent variables.
- The correlation coefficient ranges from -1 to 1, where -1 represents a perfect negative linear relationship, 0 represents no linear relationship, and 1 represents a perfect positive linear relationship.
- A positive correlation coefficient suggests that as the independent variable increases, the dependent variable tends to increase as well. Conversely, a negative correlation coefficient suggests that as the independent variable increases, the dependent variable tends to decrease.
- The closer the correlation coefficient is to 1 or -1, the stronger the linear relationship. A correlation coefficient closer to 0 indicates a weaker relationship.
To test the significance of the strength of the relationship:
- Look for the p-value associated with each independent variable in the regression model.
- The p-value measures the probability of observing the results (or more extreme results) if the null hypothesis is true.
- If the p-value is less than your chosen significance level (alpha), typically 0.05 or 0.10, you can reject the null hypothesis and conclude that there is a significant relationship between the independent variable and the dependent variable.
- If the p-value is greater than the significance level, you fail to reject the null hypothesis and interpret that there is not a significant relationship between the independent variable and the dependent variable.
Remember to consult the software's documentation or seek expert advice if you encounter any challenges while performing the regression analysis or obtaining the necessary statistics.