Multiple Regression Part 1

Multiple linear regression equations

1 DV but more than one predictor variable, can explain more variance in DV

Least squares

line that minimizes the squared errors, based on all predictors, shown by PLANE of best fit

Steps to follow when doing a multivariate regression

graph the variables, correlate the varaibles, conduct the regression

What is the equation for a multiple regression?

Yhat = b₀ (the intercept) + b₁(Age) + b₂(education) + b₃(Health)

SPSS for multivariate regression

Look for: mirroed display like a correlation table shows up first. Next the variables entered/removed table shows the enter method used. The model summary shows the R we need, which is the magnitiude of the correlations, the R square is the variance, so if .08 thta would be 8% of the DV is explained by all of the variables. The ANOVA table shows Mean Square, the residual beinf the square root of the SE of estimate. Finally, the Coeffecients table show the intercept (B as the constant in Unstandardized), slope values under standardized beta coes, and sig levels.

Intepretation: 3 possible.

1: Controlling for age (β = STNCOEBETA, p = siglvl) and self-rated health (β =.11, p = .063), people who have completed more education perform significantly better on the BDS than people with lesseducation (β = .22, p < .001).

2: Holding age (β = -.05, p = .426) and self-rated health (β = .11, p = .063) constant, people who have completed more education…

3: State #1 or #2 and then focus on R2 - Age, education, and self-rated health account for 8% of the variability in BDS scores.

Tests of regression coefficients

b and β are linear transformation of each other, if one is significant both are, based on SE, less error there is more likely to be significant, t-test is used, t = b-b* / SE

Assumptions of the distribution

multivariate normal, substantial depatures from normal and still be okay because this test is robust, conditonal dist of y (dist of y for a specific value of x) are normally and independently distributed, moderate departures are okay

Multiple correlation coefficient

uses R, correlation between DV ad all IVs at once, more interested in R² for the most part

SPSS for multiple correlation coefficient

Look for: given a model summary table. R square is effect size. After, given an ANOVA table, look for F and sig, F should be about 4 or larger as it is t squarred

How to test significance of R²

Does a set of variables predict Y better than chance, R* = correlation coefficient of population, H₀: R* = 0, p in this situation is = to the number of IVs

How to deal with issues of sample size with regressions

have at leats 10 people her IV, N should be bigger than the amount of IVs (p) by 40-50, and use power as a basis. More is better.