1. Business 205

2. Review Exam Least Square Regression Simple Linear Regression

3. Preview Multiple Regression Trends Forecasting Excel

4. Multiple Regression Using more than one IV in order to establish the relationship to the DV. Price and Store Location  Amount Sold

5. r values Correlation between variables How well the two or more variables are related

6. Coefficient of Determination (r 2 ) Proportion of variation in Y that is explained by the independent variable X

7. Residuals Estimated errors0 Difference between the observed value (Y) and the predicted value (Y p ).

8. Multiple Regression Model a dependent variable by several independent variables Has a constant random error “ε” Learn about the relationship between several IVs and a DV

9. Multiple Regression adjusted r 2 Reflects both the number of independent variables in a model and the sample size Remember:

10. ANOVA table for Regression SourcedfSum of SquaresMean SquareF Regressionk SSR k MSR MSE Errorn – k -1SSE n-k-1 Totaln - 1SST Testing if the slope of the regression line is statistically significant.

11. What can you do with Regression? Trends Forecasting

12. Excel: Regression Tools Data Analysis Regression

13. Milestone 6 Look for your “best” reliability Cronbach’s α =.83 Find the Average for each person’s survey using ONLY those questions that are reliable Sort data by group condition Run your analysis Write up the different sections

14. Entering it in Excel Create a variable for the happiness mean. When you start running your statistical analyses, you will be using the HapMean score only. NumberGenderQ1Q2Q3HapMean 1F5444.33 2M3523.33 Make sure the survey is reliable. Take the mean of the questions and only those questions that are reliable. This becomes the “happiness” score for that person.

15. Write up your Methods Section You need an Independent Variables Section and a Dependent Variables Section IV: Money a student makes DV: Satisfaction with tuition levels

16. IV write up Independent Variables Money a student makes. The independent variable was manipulated by two groups: those who made less than or equal to $10,000 a year (n = 2) and those that made more than $10,000 a year (n = 3).

17. DV write up Dependent Variables Satisfaction with tuition levels. A 5 point Likert-type scale was utilized in order to measure satisfaction. Questions were “ I believe that we are paying too much for tuition,” “States should fund more money to schools,” and “We should all protest tuition hikes” (Cronbach’s α =.83). *Only include those questions with that reliability!

18. Method Section Study Write-up A quick paragraph on how you conducted the study Since we “cheated”, you can make it up as if you really did do the study Demographic Section If you have demographic/categorical data, report it in this section

19. Method Section Example (Study) Participants (N = 5) were asked to complete a survey in class regarding how they felt about tuition hikes. Participants were randomly assigned to one of two conditions: they made $10,000 or less (n = 2) or they made more than $10,000. After they completed the survey, they were thanked and were free to leave.

20. Excel Countif Function =Countif(range, criteria) =countif(A1:A4, “f”) =countif(A1:A4, “m”)

21. Descriptive Statistics Tools Data Analysis Descriptive Statistics Be very careful with the output as it only counts how many are there, not how many are in each category within a group! Additionally, if you dummy code (0/1), it will take a mean of the dummy coded values!

22. Method Section Example (demographics) The sample (N = 5) consisted of 40% males and 60% females with an average age of 24 (M = 24.00, SD = 1.23). Participants were predominantly Caucasian (n = 4) and had stated that they drove to work (n = 3).

23. Results Section (no significance) A two independent sample t-test was conducted to see if there was a difference between amount of money a student made and how satisfied they were with a tuition hike. The results revealed no significance.

24. Results Section (significance) A two independent sample t-test was conducted to see if there was a difference between amount of money a student made and how satisfied they were with a tuition hike. The results revealed significance, t(4) = -3.00, p <.05, two-tailed.

25. Group Work Have your things ready: Survey Print out of data Reliability Hypothesis What test will you need to run?

26. The following are formulas you can use in order to find the information located in the ANOVA regression chart. You do NOT need to perform this by hand!!! These formulas are for your own edification

27. Regression Regression Sums of Squares Explained Variation for Predicted values of Y Error Sums of Squares Explained Variation for Predicted values of Y Sums of Squares Total

28. Standard Error of the Estimate Standard deviation around the prediction line; measures variability around the prediction line

29. Testing Significance Mean Square Regression k = number of independent variables in the regression model

30. Testing for Significance Mean Square Error df = (n – k – 1)

31. Testing a Linear Regression Slope Testing if the slope is statistically significant