exam 3 scatterplots, correlation coefficient, linear regression

scatterplot form

• straight line (linear)

• curved (rare)

scatterplot direction

• positive: larger X values with larger Y values

  • slopes up

• negative: larger X values with smaller Y values

  • slopes down

scatterplot strength

• determined by how closely the points follow a clear line

• increased scatter = decreased strength

outliers

• striking deviations from pattern

• strong impact on results

correlation coefficient (r) definition

describes the strength and direction of a linear relationship between two quantitative variables

range of values for a correlation coefficient (CC)

between 1 & -1 (including 0)

How value of CC indicates strength, and + or - indicates direction

• closer to 0 = very weak relationship

• closer to 1 or -1 = very strong relationship

  • 1 = upward

  • -1 = downward

no units for CC

descriptive statistics (mean, median, quartiles, standard devaition) share the same unit as the original observation

explain why correlation does not imply causation

two variables can be related without causing another

CC does not describe a curved relationship

LINEAR relationships

how outliers influence a CC

• depends on where outliers are whether it strengthens or weakens relationship

• outliers will impact CC

regression definition

mathematical equation that explains the linear relationship between two numerical variables

regression x vs y variables

• x - explanatory variable (independent/predictor)

• y - response variable (dependent/outcome)

LS method

• least squares

• the line that minimizes the su, of the squared vertical distances of the data points on the line

residual definition

vertical distances of data points from the line

• observed - predicted value

regression equations

Y = a + bx

• Y = predicted value of Y for a given X

• a = intercept of the line

• b = slope

extrapolation

if you predict beyond the limits of the observations used to create the regression equation or else it will be extrapolation

R²

tells you how strong the line of regression is

null hypothesis for regression equation

slope = 0

alternative hypothesis for regression equation

slope does not equal 0