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

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?

Range and strength of coefficient

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

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

Simple Regression

Simple Regression Y-Variable X-Variable

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.

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).

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.

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

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

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

Making the Regression Graph Using Microsoft Excel 2007

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

Making the Regression Graph Using Microsoft Excel 2007 Choose Layout 1

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

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).

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

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

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

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”

Multiple Regression Analysis Conclusion shown on the next slide…

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.

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).