1. Data Analysis Module: Correlation and Regression
R Programming
Data Analysis Module: Correlation and Regression

2. Data Analysis Module
Basic Descriptive Statistics and Confidence Intervals
Basic Visualizations
Histograms
Pie Charts
Bar Charts
Scatterplots
Ttests/Bivariate testing
One Sample
Paired
Independent Two Sample
ANOVA
Chi Square and Odds
Regression Basics

3. Data Analysis Module: Correlation and Regression
Dependent Variable
Independent (predictor) Variable
Statistical Test
Comments
Quantitative
Categorical
T-TEST (one, two or paired sample)
Determines if categorical variable (factor) affects dependent variable; typically used for experimental or planned change studies
Correlation/Regression Analysis
Test establishes a regression model; used to explain, predict or control dependent variable
Chi-Square
Tests if variables are statistically independent (i.e. are they related or not?)

4. Data Analysis Module: Correlation and Regression
Correlation coefficients assess strength of linear relationship between two quantitative variables.
The correlation measure ranges from -1 to +1.
A negative correlation means that X and Y are inversely related.
A positive correlation means that X and Y are directly related.
zero correlation means that X and Y are not linearly related.
A correlation of +1 indicates X and Y are directly related and that all the points fall on the same straight line.
A correlation of -1 indicates X and Y are inversely related and that all the points fall on the same straight line
Plot Scatter Diagram of Each Predictor variable and Dependent Variable
Look of Departures from Linearity
Look for extreme data points (Outliers)
Examine Partial Correlation
Can’t determine causality, but isolate confounding variables

5. Data Analysis Module: Correlation and Regression
For example, lets take two variables and evaluate their correlation…open the stats98 dataset in Excel… What would you expect the correlation of the Verbal SAT scores and the Math SAT scores to be? Why? What would you expect the correlation of the Math SAT scores and the percent taking the test to be? Why?

6. Data Analysis Module: Correlation and Regression
What would you expect the correlation of the Verbal SAT scores and the Math SAT scores to be? Why?

7. Data Analysis Module: Correlation and Regression
What would you expect the correlation of the Math SAT scores and the Percent of HS students that took the test? Why?

8. Data Analysis Module: Correlation and Regression

9. Data Analysis Module: Correlation and Regression
From the previous slide, the “regression line” has been imposed onto the relationship between Price and Age of car.
The equation of this line takes the general form of y=mx+b, where:
Y is the dependent variable (Price)
M is the slope of the line
X is the independent variable (Age)
B is the Y-intercept.
When we discussion regression models, we transform this equation to be:
Y = bo + b1x1 + …bnxn
Where bo is the y-intercept and b1 is the slope of the line. The “slope” is also the effect of a one unit change of x on y.

10. Data Analysis Module: Correlation and Regression
From the previous slide, the model equation is presented in the form of the equation of a line: y=-924x
From this, we would say:
For every 1 year of a car’s age, there is a $924 decrease in theprice of the car.
Every car “starts” at $12,320.
If a car is 2 years old, the expected price is $10,472.
That R2 value of is interpreted as “89.37% of the change in price of the cars can be explained by this linear model, where age is the only predictor”.