1. Exploring relationships between variables Unit 2 Scatterplots, Associations, and Correlations

2. Scatterplots • 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)

4. Z-scores • 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

6. variables • 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

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)

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

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

11. Complete problem 4 on page 160

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

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

14. Confidence Intervals • 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

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

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