Unit 2: Correlation and Regression

Unit 2: Correlation and Regression

1. Intro: Consider relationship b/w 2 variables x and y (x= height, y= weight)

2. 1. Scatter Diagram: Plot y values on vertical axis and x values on horizontal axis

3. 2. Correlation: The relationship b/w x & y.

   • The correlation of coefficient r is a #b/w -1 and +1 and measures the linear relationship b/w x and y values.
     • Positive: If x and y values lie on a straight line with positive slope. Here R=+1 (and x increases, y increases).
     • Negative: If x and y values lie on a straight line with a -1 slope, there is a 'negative' relationship b/w x and y.
     • No Relationship: If there is no linear relationship, R=0
     • Equations: (n= # pairs of values)

4. 3. Linear Regression

   • Least Squares Regression Model: Suppose x effects y values, and we want to model this straight line relationship. We fit a line y=a+bx to fit the data. We have to estimate a and b. (the data wont lie exactly on the straight line). For each value where x-xi, y=yi.
   • Residual (ri): The difference b/w xi or yi from y= a+bx. It is expressed as ri= yi-(a+bxi)
   • Residual Sum of Squares: When we estimate a and b to make the sum of ri^2 as small as possible

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