MR Final - Chapter 15

Variance inflation factor (VIF)

- Can be used to assess and *eliminate multicollinearity by seeing which ind. variable contributes to it/ to removed* • VIF is a statistical value that identifies what independent variable(s) contribute to multicollinearity and should be removed • Any variable with VIF of *greater than 10 should be removed*

Multiple R:

- also called the coefficient of determination - is a measure of the strength of the overall linear relationship in multiple regression - It indicates how well the independent variables can predict the dependent variable - ranges from 0 to +1 and represents the amount of the dependent variable that is "explained," or accounted for, by the combined independent variables CD SL IPD

Bivariate regression

- means *only two variables are being analyzed* - researchers sometimes refer to this case as "*simple regression*"

Multiple regression analysis

- means that you have *more than one independent variable to predict a single dependent variable* - uses the *same concepts as bivariate regression analysis, but uses more variables* than one independent variable - With multiple regression, the *regression plane = shape of the dependent variables* (page 4 & 5)

Independence assumption

- the independent variables must be statistically independent and uncorrelated with one another (the presence of strong correlations among independent variables is called multicollinearity) *independent variables must have no multicollinearity* (independent and not correlated)

Stepwise regression is useful when: (2)

- there are *many independent variables* - researcher wants to *narrow the set down* to a smaller number of statistically significant variables

Basic Assumptions of Multiple Regression (3)

1. Independence assumption 2. Variance inflation factor (VIF) 3. Additivity

3 Warnings Regarding Multiple Regression Analysis

1. Regression is a statistical tool, *not a cause-and effect statement* 2. Regression analysis *should not be applied outside the boundaries* of data used to develop the regression model 3. Chapter 15 is simplified...regression analysis *is complex* and requires additional study

Name the 4 facts that are true of regression.

1. Use independent variable to predict the dependent variable 2. There is no cause-and-effect relationship or true dependence between the dependent and the independent variable 3. straight-line equation is the basis of regression analysis 4. in bivariate regression only two variables are involved in the predictive model

What are the elements in the straight line formula? (4)

1. x= the variable used to predict y 2. y= the predicted variable 3. b= the slope or the change in y for any 1 unit change in x 4. a= the intercept, or point where the line cuts the y axis when x=0 y = a + bx

In the straight-line equation y = a + bx, y is the independent variable. (T/F)

False

The independence assumption is not overly important in multiple regression. (T/F)

False

What regression analysis means that you have more than one independent variable to predict a single dependent variable?

Multiple regresion analysis

What does the "m" in the multiple regression equation stand for? y = a + b1x1 + b2x2 + b3x3 + ... + bmxm

The number of independent variables in the equation

An important application of multiple analysis is as an identifying or screening device. (T/F)

True

An outlier is a data point that is substantially outside the normal range of the data points being analyzed. (T/F)

True

Stepwise regression is useful if a researcher has many independent variables and wants to narrow the set down to a smaller number of statistically significant variables. (T/F)

True

Regression analysis

a predictive analysis technique in which one or more variables are used to *predict the level of another by use of the straight-line formula*

What is defined as a variable that is scaled with a nominal 0 versus 1 coding scheme.

dummy independent variable

A general conceptual model identifies...

independent and dependent variables and shows their basic relationships to one another

What is the way of guaranteeing the straight line that runs through the points on a scatter diagram is positioned so as to minimize the vertical distances away from the line of the various points?

least squares criterion

A(n) _____________ is a structure that ties together various constructs and their relationships

model

________________ is a predictive analysis technique in which one variable is used to predict the level of another by use of the straight-line formula

regression analysis

multicollinearity

statistically independent and not correlated with another variable

Dependent variable:

that which is predicted (y in the regression straight-line equation)

What is the process called whereby a researcher systematically eliminates the nonsignificant independent variables in multiple regression analysis?

trimming

Independent variable:

used to predict the independent variable (x in the regression straight-line equation)

Special Uses of Multiple Regression (3)

• *Dummy independent variable*: scales with a nominal coding scheme 0- versus-1 • Using *standardized betas to directly compare independent variables*: allows direct comparison of each independent value • Using *multiple regression as a screening device of which to exclude*: identify variables to exclude

Improving Regression Analysis

• *Identify any outlier* -- a data point that is substantially outside the normal range of the data points being analyzed

Most important when used as a screening devise:

• Dependent variable • Statistically significant independent variables • Signs of beta coefficients • Standardized bets coefficients for significant variables DSBS

Additivity

• The inclusion of each independent variable preserves the straight-line assumptions of multiple regression analysis - This is sometimes known as additivity because each new independent variable is added to the regression equation

Stepwise Multiple Regression

• The one independent variable that is statistically significant and explains the most variance is entered first into the multiple regression equation. • Then, each statistically significant independent variable is *added in order of variance explained* • All *insignificant independent variables are excluded*

Bivariate Linear Regression Analysis

• With bivariate analysis, *one is used to predict another* variable • The *straight-line equation = basis of regression analysis* (math on 1-3)

"Trimming" the Regression

• means that you *eliminate the nonsignificant independent variables and, then, rerun the regression* • trimmed regressions iteratively *run until all betas are significant* • The resultant regression model expresses the salient independent variables