Correlation and Simple Regression and Multiple Regression

covariance

how two variables “vary together”, average squared distance of data points from the mean

what is the numerical range of covariance

infinity to negative infinity

correlation

standardized version of covariance

simple regression

deals with one continuous X and one continuous Y variable

intercept (simple regression)

value of Y when X = 0

slope (simple regression)

change in Y given a one point increase in X

equation of a line

Y = b0 + b1(x) + e

what does e equal in the equation of a line

error

what goal should a line have in simple regression

minimize error

what is the maximum likelihood for drawing the line

goes through the values of b0 and b1 until it finds the best possible solution

ordinary least squares

formulae developed to mimic (exactly) maximum likelihood under the right conditions

what are the three main steps of regression practice

collect “validation data”, use data to estimate the regression line, use the regression line to predict performance of new employees (ex)

multiple regression

one continuous Y (outcome), more than one continuous X (predictor) variable

univariate regression model

they only have one outcome (Y)

what can regression models be captured succinctly using

path diagrams

intercept (multiple regression)

value of Y when all Xs = 0

clope (multiple regression)

change in Y given a one point change in X holding all other Xs are 0

R command for running a regression model

LM (linear model)