AMS 5 Lecture Notes - Lecture 7: Joule, Shoe Size, Confounding

• School: UCSC
• Department: Applied Math and Statistics
• Course: AMS 5
• Professor: Yonatan Katznelson

Document Summary

Associations: weak, strong (less outliers, positive, negative, no obvious (linear) relationship. Comments: the relation between two variables is often complicated. In particular, many dependent" variables depend on more than just one independent" variable. This can make understanding the relation between just two variables more difficult. In many cases, a complicated relation between two variables can be approximated by a linear relation: want: a number that characterizes the nature and strength of the (linear) relation between two variables. If the relation between x and y is positive, then above-average x-values will tend to be paired with above-average y-values and below-average x-values will tend to be paired with below-average y-values. The correlation coefficient: the correlation coefficient r(xy) of a set of paired data, {(x1, y1), (x2, y2), ,(xn, yn)} is defined by r(xy) = 1/n z(xj)*z(yj) [ = summation: observation: (x(j)-x)/sd(x) = z(xj) is the score of x(j) and (y(j)-y)/sd(y) = z(yj) is the z- socre of y(j).