EXS 407 exam 2: multiple regression

What does a coefficient of determination (r²) of 0.73 indicate?

It indicates that 73% of the variance in the dependent variable is explained by the independent variables.

What is multiple correlation?

It quantifies the degree of relationship/association between a function of independent variables and one dependent variable

-represented by a coefficient (R) between 0.00 and 1.00.

What does an R value of 0.00 signify?

It signifies no correlation or relationship between independent variables and the dependent variable.

What does an R value of 1.00 signify?

It signifies a perfect correlation where independent variables completely explain the dependent variable.

What is partial correlation?

It quantifies the relationship between an independent variable and a dependent variable after removing the effect of another variable (covariate).

r^2yx1,x2=partial coefficient of determination: variance in Y explained by X1 after removing the effects of X2 on both

What are the assumptions for using multiple/partial correlation?

1. Continuous (interval or ratio) scale for both variables

2. Independence of variable pairs

3. Approximate normal distribution of both variables

4. Linear relationship between variables

5. No outliers

What is the purpose of multiple linear regression?

To predict one dependent variable from multiple predictor variables and find the most satisfactory equation for prediction of the DV (lowest SEe)

-more predictor variables can increase or not change the predictive power

What is the general form of a multiple linear regression equation?

Y = a + b1X1 + b2X2 + ... + bkXk, where Y is the dependent variable, a is the Y-intercept, and b's are the slope coefficients.

What is hierarchical multiple regression?

-the researcher controls the model equation and which predictors are included

-often used for hypothesis testing (not DV predictions)

What is forward selection in multiple regression?

A method that starts with the intercept only and adds predictors one-by-one based on their contribution to the model.

What is backward elimination in multiple regression?

A method that starts with all predictors and eliminates them one-by-one based on their contribution to the model.

What is stepwise regression?

A method that starts with just the intercept, then combines forward selection and backward elimination, allowing previously entered variables to be removed.

process of forward selection

IV with the strongest correlation (highest r) to the DV is added first

-the IV that increases r^2 the most is added next (explains the most unique variance)

-continue with the next strongest r^2

process of backward elimination

-all IV are added initially

-IVs are eliminated in order that their removal decreases explained variance the least, stop when theres a significant reduction in explained variance

Process of Stepwise Regression

-IVs are added as in forward selection, but they can be eliminated if the r^2 is not affected

-con: need a larger sample size

assumptions of multiple regression

1. Linear relationships

2. Independent variables

3. Approx normally distributed

4. The variance of the residuals must be consistent across the range of IV values (homoscedasticity)

5. Independent variables should not be correlated with each other (multicollinearity)

What is multicollinearity?

It occurs when independent variables are correlated with each other= inflated confidence intervals and unstable coefficient estimates (B1 is meaningless)

-no threshold of acceptable multicollinearity, but VIF>10 is suspicious

-ideally there is no correlation of IVs (explain unique amounts of variability)

What is the variance inflation factor (VIF)?

A measure used to detect multicollinearity; a VIF greater than 10 is considered suspicious.

singularity

two IVs are perfectly related, r=1, usually because one was derived from the other

What is cross-validation in regression analysis?

A process of testing regression equations on a separate sample to ensure accuracy in predictions.

-can accomplish by splitting dataset in half and running model on the other half

What is the expected outcome when applying models to different samples?

Higher prediction errors are expected because the model is optimal for the training data.

-the multiple correlation coefficient undergoes shrinkage

What statistic is used to make decisions about adding or removing predictors in regression?

r^2

What is the significance of the slope coefficients in a regression equation?

They represent the weight or impact of each independent variable on the dependent variable.

What does the term 'unexplained variance' refer to in regression analysis?

It refers to the portion of variance in the dependent variable that is not accounted for by the independent variables.

What is the importance of checking for outliers in regression analysis?

Outliers can distort correlation coefficients and affect the reliability of the regression model.