1. Exploring relationships between variables Ch. 10 Scatterplots, Associations, and Correlations Ch. 10 Scatterplots, Associations, and Correlations

2. Scatterplots Shows change over time Shows patterns Shows Trends Relationships Outlier values Shows change over time Shows patterns Shows Trends Relationships Outlier values

3. Scatterplots Can be positive or negative Show relationship amongst 2 variables Can be shown more in depth through the Z-scores of both variables (ZX, ZY) Can be positive or negative Show relationship amongst 2 variables Can be shown more in depth through the Z-scores of both variables (ZX, ZY)

4. Z-scores X-MeanX / Standard Deviation (SX) Y-MeanY / Standard Deviation (SY) Calculating standard deviation in the same way as before. X-MeanX / Standard Deviation (SX) Y-MeanY / Standard Deviation (SY) Calculating standard deviation in the same way as before.

5. Ratio Correlation coefficient Sum of SX * SY / n-1 Correlation measures the strength of the linear association between 2 variables Correlation coefficient Sum of SX * SY / n-1 Correlation measures the strength of the linear association between 2 variables

6. variables Explanatory Variable – X Response Variable - Y Explanatory Variable – X Response Variable - Y

7. Least-Squares Line Y= a + bx a = y intercept b = slope a = y – bx b = SSxy/SSx SSx = Sum of squares of x Y= a + bx a = y intercept b = slope a = y – bx b = SSxy/SSx SSx = Sum of squares of x

8. SSx This is calculated by obtaining the sum of each squared x You then subtract the sum of x squared divided by n You can get SSx on the calculator by squaring the standard deviation then multiplying it by (n-1) This is calculated by obtaining the sum of each squared x You then subtract the sum of x squared divided by n You can get SSx on the calculator by squaring the standard deviation then multiplying it by (n-1)

9. SSxy Sum of squares of x and y Take the sum of each x value times each y value. You then subtract from that total the (Sum of x) * (Sum of y) n Sum of squares of x and y Take the sum of each x value times each y value. You then subtract from that total the (Sum of x) * (Sum of y) n

10. SSxy SSxy is a more efficient way of computing Sum of each (x-xbar) * (y-ybar) SSxy is a more efficient way of computing Sum of each (x-xbar) * (y-ybar)

11. Complete Guided Ex. #3 page 566

12. Standard Error of Estimate Se = square root of E(y-yp)squared/n – 2 How to calculate square root of SDY – b(SDx * SDy) / n-2 Se = square root of E(y-yp)squared/n – 2 How to calculate square root of SDY – b(SDx * SDy) / n-2

13. Residuals You can graph the residual of the equation to see if the regression is accurate Residuals are the difference between the observed value and the predicted value R = observed - predicted You can graph the residual of the equation to see if the regression is accurate Residuals are the difference between the observed value and the predicted value R = observed - predicted

14. Confidence Intervals Yp – E < y < yp + E Yp = predicted value of y Yp – E < y < yp + E Yp = predicted value of y

15. What does this mean (better understanding)

16. Types of data Outlier Leverage Influential Point Lurking Variable Outlier Leverage Influential Point Lurking Variable

17. Outlier Any data point that stands away from the others

18. Leverage Data points with X-values that are far from the mean Can alter the line of least regression Data points with X-values that are far from the mean Can alter the line of least regression

19. Influential Point Omitting this point can drastically alter the regression model

20. Lurking Variable A variable that is hidden in the equation It is not explicitly part of the model but affects the way the variables in the model appear A variable that is hidden in the equation It is not explicitly part of the model but affects the way the variables in the model appear