linear regression

what does linear regression provide

a means to estimate or predict the value of a dependent variable based upon the value of one or more independent variable

what is the regression equation

a mathematical expression of a causal proposition emerging from a theoretical framework

when is the the link between the theoretical statement and the equation made 

prior to data collection and analysis 

linear regression is the statistical method of

estimating the expected value of y given the value of x

simple linear regression

involves the use of one independent variable

multiple linear regression

involves the use of more than one independent variable

the regression line developed from simple linear regression is usally

plotted on a graph

Horizontal axis represents

X- independent

Vertical axis represents

Y- dependent

y-intercept

A

slope or the coefficient of x

B

what does the slope determine

the direction and angle of the regression line within the graph

what does the slope express

the extent to which y changes for every one-unit change in x

what score of variable y is predicted

from the subjects known score on variable x

what does simple linear regression explain

the dynamics within a scatterplot

how to explain the dynamics within a scatterplot

by drawing a straight line through the plotted scores

can any single regression line be used to predict with complete accuracy, every y value from every x value

no

the line of best fit

purpose is to develop the line to allow the highest degree of prediction

possible

method of least squares

procedure for developing the line of best fit

what would happen if all data were perfectly correlated

all data points would fall along a stright line or line of best fit

what does the line of best fit provide

the best equation for the values of y to be predicted

how can the line of best fit make best equation for the values of y to be predicted

by locating the intersection of points on the line for any given value of x

Algebraic equation for the regression line of best fit is

y=bx+a

y=bx+a

– y = dependent variable (outcome)

– x = independent variable (predictor)

– b = slope of the line (regression coefficient)

– a = y intercept (regression constant)

what is multiple linear regression

An estimation of simple linear regression in which more than one independent variable is entered into the analysis to predict a dependent

variable

assumptions of multiple regression

– The independent variables are measured with minimal error

– Variables can be treated as interval or ratio level measures

– The residuals are not correlated

– Dependent variable scores are normally distributed

– Scores are homoscedastic or equally-dispersed about the line of best fit

– y scores have equal variance at each value of x

what do researchers often correlate with multiple independent variables

the independent variables with the dependent variable

why do researchers often correlate the independent variables with the dependent variabl

to determine which independent variables are most highly correlated with the dependent variable

To be effective predictors what do independent variables need to have

strong correlations with the dependent variables but only weak correlations with the other independent variables in the equation

when does multicollinearity occur

when the independent variables in the multiple regression equation are strongly correlated

R²

one of the outcomes from a multiple regression analysis

With the addition of each independent variable to the regression formula

a change in R² is reported 

what is R² used to calculate

the percentage of variance that is predicted by the regression formula

for R² what is the significance tested with

ANOVA