1. Statistics Class 7 2/11/2013

2. It’s all relative. Create a box and whisker diagram for the following data(hint: you need to find the 5 number summary): 53, 62, 78, 94, 96, 99, 103, 58, 97, 77, 64, 101

3. Correlation A correlation exists between two variables when the value of one variable are somehow associated with the values of the other variable.

4. Correlation

5. The Linear coefficient r measure the strength of the linear correlation between the paired quantitative x- and y- values in a sample. (The linear correlation coefficient is sometimes called the Pearson product moment correlation coefficient in honor of Karl Pearson who developed it).

6. Correlation Calculating the linear coefficient r Requirements 1.The sample data (x,y) is paired. 2.Visual examination of the scatterplot must confirm that the points approximate a straight-line pattern. 3.Since results may strongly affected by the presence of outliers, any outliers must be removed if they are known to be errors. The effects of any other outliers should be considered by calculation r with and without the outliers included

7. Correlation

8. Properties of the Linear Correlation Coefficient r 1.The value of r is always between -1 and 1 inclusive. 2.If all values of either variable are converted to a different scale, the value of r does not change 3.The value r is not affected by the choice of x or y. So if you interchange all x- and y- values the value of r will not change 4.r measure the strength of a linear relationship. It is not designed to measure the strength of a relationship that is not linear. 5.r is very sensitive to outliers in the sense that a single one can dramatically affect its value.

9. Correlation Ex 2. Look at all the work involved to calculate r by hand using the long formula. Cost of Pizza0.150.351.001.251.752.00 Subway Fare0.150.351.001.351.502.00

10. Correlation Ex 2. Look at all the work involved to calculate r by hand using the long formula. Ex 3. Look at all the work involved to calculate r by hand using the short formula. Note: That the long formula is more precise, and the shortcut formula is really only used to give an idea of what r is. Cost of Pizza0.150.351.001.251.752.00 Subway Fare0.150.351.001.351.502.00

11. Correlation Cost of Pizza0.150.351.001.251.752.00 Subway Fare0.150.351.001.351.502.00

12. Correlation

13. We should get

14. Correlation

17. Common Errors 1.A common error is to conclude that correlation implies causality. 2.Another error arise with data based averages. Averages suppress variation and may inflate the correlation coefficient 3.If there is no linear correlation, there still might be some other correlation that is not linear.

18. Correlation