# Understanding Regression: Linear Regression, Multiple Regression

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Part 1 - Understanding Regression Terminology

Create a handout for students in an introductory statistics course which summarizes the following regression terms (in your own words):

o R2 versus Adjusted R2

o Beta

o Regression Coefficient

o Hierarchical Regression

o Multi-collinearity

o Curvilinear

o Homoscedasticity

o Outlier

o Ordinary least squares

o Residual

Part 2 - Simple Linear Regression

An organization wants to use interview scores to predict performance in an employee development program. Review the regression results in Figure 5 attached.

Figure 5. Summary output from a simple linear regression analysis produced by Excel. The results are organized in three tables - 1) regression statistics including the R squared, standard error, and number of observations, 2) ANOVA F-tests for the regression model and residuals, 3) and significance tests for the coefficients.

o Are the results significant? Explain your response.

o Use the summary output to find the least square regression line: y = ax + b

o Jeff Jones has an interview score of 3.4. Estimate the value of y (performance) when x = 3.4.

Part 3 - Multiple Regression

The organization wants to use a combination of interview scores (x1), scores from a role playing exercise (x2), and personality test scores (x3) to predict performance (y) in the employee development program. An I/O psychologist collected data on the 32 employees who have already participated in the program. The employee data are presented in the Data file. Open the file to the Employee Summary tab.

1. Run a multiple regression analysis in Excel

2. Copy the summary output (Regression Statistics Table, ANOVA Table, and Coefficient Table) into a Word document.

3. Are the results significant? Explain your response.

4. Should all predictors be included in the least squares regression line? Should any predictors be excluded? Why or why not?

5. Use the summary output to find the least square regression line: y = ax1 + ax2 + ax3 +b

6. Estimate the y (performance) for the following two candidates (show your work):

Interview Score Role Play Score Personality Test Score

Laura 5 4 45

Gary 4 5 40

7. Based on these results which candidate would you select into the employee development program?

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##### Solution Summary

This solution consists of details of performing a multiple linear regression analysis using Excel.

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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