Chapter 4:Regression Analysis Review of Last Lecture:  Box plots are best looked at in groups(for comparison) o This allows us to see whether variables have positive, negative, or neutral o Box plots are usually used with numeric and categorical data Scatterplots  Used to investigate positive, negative or neutral association between 2 numerical values Also used to see whether association between two variables is positive, negative, or neutralPositive Trends in scatterplots  As one variable increases so does the other  Does not mean good or bad For example: large cars are wide and short cars are narrowo There is positive association between length and width Negative Trends As one variable increases the other decreases  Example: heavy cars have lower MPG and light cars have lighter MPG o There is negative association between weight an MPGNo Trend(neutral) There is no clear association  Example: the size of a student body doesn’t predict the average test scoreo There is no correlation or association between the size of a student body and their test scores Strength of Association If for every x value there are a small spread of y values (i.e. if y values are not spread out) correlation between x and y is weak If there is weak association between x and y, x is a bad predictor of yLinear Trends Points generally stay on a line Linear trend are the easiest to work with Non-Linear Trends  Covered in advanced stats Scatterplots  Check to make sure if there is a trend of associationo Weak or strong association?o Is it linear or non linear? Measuring Association: The Correlation Coefficient “r” r measures the linear strength between two variables r represents values from -1 to 0 to 1 if r is a value closer to +1 there is strong positive linear associationo examples of r with positive association: 1, .72, and .04  if r is a value closer to -1 there is a strong negative associationo examples of r with negative association: -.56, -.9, and -1.0 examples of r with neutral association: .19, .00, and -.35Switching x and y switching x and y has no effect on RCorrelation, Transformations, and Units  multiplying all x’s and y’s by the same constant doesn’t change r value  adding the same constant to x and y doesn’t change r value  changing units (inches  cm) doesn’t change r value  r is unitless Correlation, Linearity, and Outliers  linear correlation only used when data has a linear relationship o outliers have a strong effect on