1. 3.3 Correlation: The Strength of a Linear Trend Estimating the Correlation Measure strength of a linear trend using: r (between -1 to 1) Positive, Negative or 0 Closer to -1 or 1, the stronger the correlation Average product of the z-scores r has no units Because z has no units D9, D10, pg. 141

2. 3.3 Correlation: The Strength of a Linear Trend Correlation and the Appropriateness of a Linear Model Even though r may be very close to 1 or -1, you cannot assume a strong linear model. Always graph your data to make sure the scatter plot shows a linear trend. Even though r is close to 0, it doesn’t say there is not a linear trend – just that the strength of the trend is weak.

3. 3.3 Correlation: The Strength of a Linear Trend The Relationship between Correlation and Slope The slope of a least squares line, b 1, and the correlation, r, are related by the equation This means if you standardize the data so that s x =1 and s y =1, then the slope of the regression line is equal to the correlation. D17, pg. 147

4. 3.3 Correlation: The Strength of a Linear Trend Correlation Does Not Imply Causation LURKING VARIABLE Beware of the LURKING VARIABLE A variable you didn’t include in your analysis that might explain the relationship between the variables you did include. That is, when x and y are correlated, it might be because both are consequences of a third variable, z, that is lurking in the background. why The value of r does not tell you anything about why two variables are related. D18, D19, D20 pg. 147