# Case Study Regression Equations

The case study is a written report, and it should include an introduction, your responses to the questions being asked, and a conclusion. Remember, the case study is more than just a collection of Excel output, and it should be written in complete, grammatically correct sentences. You should submit two files, a word file and an Excel file that shows your inputs. Students who submit only one file will receive a grade of zero.

In this case (Major League Baseball Team Values), you have three variables: Value as a dependent variable, Revenue as the first independent variable and Income as the second independent variable. Although you have two independent variables, remember that this case deals with Simple Linear Regression in which you will perform the regression analysis with only one dependent variable and one independent variable at each time. Therefore, the regression equations can be expressed as follow:

yË? = bo + b1 Revenue

yË? = bo + b1 Income

Question 1 asks to develop numerical and graphical summaries of the data. Therefore, you should perform descriptive statistics explained in chapter 3 for the dependent and independent variables. These descriptive statistics include: Mean, Standard Error, Median, Mode, Standard Deviation, Sample Variance, Minimum, Maximum, Sum, and Count. In addition, remember to show two scatter diagrams. The first scatter diagram shows the relationship between Value as the dependent variable and Income as the independent variable. The second scatter diagram shows the relationship between Value as the dependent variable and Revenue as the independent variable. When you draw scatter diagrams that show the relationships between Value as the dependent variable and Income as the independent variable, and Value as the dependent variable and Revenue as the independent variable, please make sure that the independent variable is placed in the first column while the dependent variable is placed in the second column. The headers at the top of each column are not necessary, but they do help identify the variables.

Question 2 asks to perform a regression analysis to investigate the relationship between Value as the dependent variable and Income as the independent variable. Therefore, the regression equation can be expressed as follow:

yË? = bo + b1 Income

In addition, you should perform a hypothesis testing assuming that ? = .05 and determine if the null hypothesis should or should not be rejected based on the following hypotheses:

H0: B1 = 0. Ha: B1 ? 0.

A null hypothesis usually states that there is no relationship between the two variables. While the alternative hypothesis usually states that there a significant relationship between the two variables. As a researcher, you want to show that the p-value is less than or equal to the alpha level. Therefore, you reject the null hypothesis and conclude that there is a significant relationship between the dependent and the independent variables. When you perform hypotheses testing, you don't need to use Excel. Formulate the null and alternative hypotheses as explained above, then you need to get the P-value for the independent variable from the Excel regression output and compare it to alpha level. If the P-value is less than or equal alpha then reject the null hypothesis.

Question 3 asks to perform a regression analysis to investigate the relationship between Value as the dependent variable and Revenue as the independent variable. Therefore, the regression equation can be expressed as follow:

yË? = bo + b1 Revenue

In addition, you should perform a hypothesis testing assuming that ? = .05 and determine if the null hypothesis should or should not be rejected based on the following hypotheses:

H0: B1 = 0.

Ha: B1 ? 0.

A null hypothesis usually states that there is no relationship between the two variables. While the alternative hypothesis usually states that there a significant relationship between the two variables. As a researcher, you want to show that the p-value is less than or equal to the alpha level. Therefore, you reject the null hypothesis and conclude that there is a significant relationship between the dependent and the independent variables. When you perform hypotheses testing, you don't need to use Excel. Formulate the null and alternative hypotheses as explained above, then you need to get the P-value for the independent variable from the Excel regression output and compare it to alpha level. If the P-value is less than or equal alpha then reject the null hypothesis.

#### Solution Summary

A case study for regression equations are examined.