1. Regression Must have Interval or Ratio scaled measures
Pearson correlation coefficient: Statistical measure of the strength of a linear relationship between two metric variables
Varies between – 1.00 and 1.00
0 represents absolutely no association between two variables
– 1.00 or 1.00 represent a perfect link between two variables
Correlation coefficient can be either positive or negative
Must have Interval or Ratio scaled measures

2. Correlation Coefficient
This helps to see if two variables correlate together.
It does not imply causality…one variable does not cause the behavior of the other variable.
Only if two variables tend to relate to each other.
Compares two continuous numbers or constructs.
For example, is there a relationship between people who like premium ice cream and people who enjoy eating in ice cream shops?

3. Range and strength of coefficient

4. Simple Regression
I like to use the regression option in SPSS to find correlations because it tells me if that correlation is significant or not.
Could I with some degree of confidence state that two variables are related to each other?
Hint: look for significance and R square

5. Types of relationships
Satisfaction and likelihood to recommend or perception
Height and weight
Sales and advertising medium
Preference for something and impact of something else (premium ice cream and eat at the shop)
Price increase impact on sales, other variables impact on sales

6. Simple Regression

7. Simple Regression
Y-Variable
X-Variable

8. Simple Regression Model Summary .572 .328 .310 1.21487 Model 1 R
R Square
Adjusted
Std. Error of
the Estimate
Predictors: (Constant), like shop construct a.
ANOVA b
27.316 1
18.508
.000 a
56.084 38
1.476
83.400 39
Regression
Residual
Total
Model
Sum of
Squares df
Mean Square F
Sig.
Predictors: (Constant), like shop construct a.
Dependent Variable: premium ic construct b.

9. Simple regression
Results: Using a regression analysis with α = .05, we found that there is a positive correlation between liking premium ice cream and eating out at ice cream shops (R2=.328, F=18.505, p<.001).

10. Simple Regression (Showing a Graph)
Showing a graph is helpful, only if the relationship is obvious and clear.
Scatterplots are generally shown by SPSS but on a report, a line from the scatterplot looks better.

11. Simple Regression (Showing a Graph)
I would NEVER show this graph in a paper!
This is only an example to show what a scatterplot looks like!
SPSS Example of the Graph

12. So…How do we Create a Regression Graph Using Excel?
Regression Equation: Y = ax+b
“a” or “slope”

13. Making the Regression Graph Using Microsoft Excel 2007
Y= ax+b a x ax b Y
0.572 1 2
1.144 3
1.716 4
2.288 5
2.86 6
3.432 7
4.004

14. Making the Regression Graph Using Microsoft Excel 2007

15. Making the Regression Graph Using Microsoft Excel 2007
Click the arrow in “chart layouts”

16. Making the Regression Graph Using Microsoft Excel 2007
Choose Layout 1

17. Making the Regression Graph Using Microsoft Excel 2007
Double click on “Axis Title” and the chart title to make appropriate changes

18. Making the Regression Graph Using Microsoft Excel 2007
Even though you have a graph, you must still show the following: We found that there is a correlation between liking premium ice cream and eating out at ice cream shops (R2=.328, F=18.505, p<.001).

19. Multiple Regression Analysis
Purpose is to test the linear relationship between 1 dependent variable and multiple independent variables.

20. Types of relationships
Better understand and predict customer satisfaction- look at perception of price, employees, atmosphere, service.
Sales and different types of advertising mediums such as TV, radio, direct mail, online

21. Statistical Significance
Not all independent variables will be statistically significant, this means the independent variable does not have a relationship with the dependent variable.

22. Multiple Regression Analysis
The steps are exactly the same, except you put in multiple independent variables.
The purpose is to find out which independent variables are the most important when predicting the dependent variable.
Change to “Stepwise”

23. Multiple Regression Analysis
Conclusion shown on the next slide…

24. Steps to analysis
Assess significance of the model in the Anova Summary and F statistic
Evaluate how large the R2
Examine each independent variable for significance or not
The size of coefficient beta show how strongly each independent variable is related to the dependent variable.

25. Reporting the Multiple Regression Analysis
If you want to show a chart, this is what it should look like
Show a table like the one below.
Variables Β t
Sig.
Quality Teaching
0.287
6.016
<.001
Discipline
0.275
6.112
Sports
0.118
2.761
.006
AP Classes
0.112
2.506
.013
Conclusion: The variables quality teaching, discipline, sports, and advanced placement classes are highly correlated with parents’ commitment to the Catholic School System. (R2=.400, F=77.181, p<.001).