1. Data Analysis and Statistical Software I (323-21-403) Quarter: Autumn 02/03
Daniela Stan, PhD
Course homepage:
Office hours: (No appointment needed)
M, 3:00pm - 3:45pm at LOOP, CST 471
W, 3:00pm - 3:45pm at LOOP, CST 471
11/10/2018
Daniela Stan - CSC323

2. Outline Chapter 2: Looking at Data – Relationships between
two or more variables
Least - Squares Regression
Cautions about Regression and Correlation
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Daniela Stan - CSC323

3. Regression
A regression line is a straight line that describes how a response variable y changes as an explanatory variable x changes.
11/10/2018
Daniela Stan - CSC323

4. Regression y = a + b*x b = slope ~ rate of change a = intercept (x=0)
Fitting a line to data means drawing a line that comes as close as possible to the points:
y = a + b*x
b = slope ~ rate of change
a = intercept (x=0)
Height= a + b*age
11/10/2018
Daniela Stan - CSC323

5. Prediction
Use of Regression: to predict the value of y for any value of x by substituting this x into the equation of the regression line.
Extrapolation is the use of regression line for prediction outside the range values of the explanatory variable x that you used to obtain the line.
Such predictions are often not accurate.
Example: Problem 2.35
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Daniela Stan - CSC323

6. The regression line makes the prediction errors as small as possible.
Least - Squares Regression
How do we fit a line to a scatterplot?
The regression line makes the prediction errors as small as possible.
11/10/2018
Daniela Stan - CSC323

7. Least - Squares Regression (cont.)
The least - squares regression line of y on x is the line
that makes the sum of the squares of the vertical distances
of the data points from the line as small as possible.
How to calculate the least – squares regression line?
= predicted value
Where:
r = correlation,
Sx,Sy = standard deviations
= means
11/10/2018
Daniela Stan - CSC323

8. Correlation and Regression
The correlation r is the slope of the least-squares regression line when we measure both x and y in standardized units.
The square of the correlation, r2
11/10/2018
Daniela Stan - CSC323

9. Cautions about regression and correlation
Residuals = the difference between the observed and predicted values of y.
A residual plot is a scatterplot of the regression residuals against the explanatory variable; it helps us to asses the fit of the regression line.
Lurking variable is a variable that is not among the explanatory or response variables in a study and yet may influence the interpretation of the relationships among those variables.
11/10/2018
Daniela Stan - CSC323

10. Data Mining
Exploring really large data bases in the hope of finding useful patterns is called data mining.
Domain
Understanding
Data Selection
Cleaning &
Preprocessing
Knowledge
Evaluation &
Interpretation
Discovering
patterns
The entire process is iterative and interactive.
11/10/2018
Daniela Stan - CSC323