Term
| Define what Stepwise Regression is |
|
Definition
Stepwise – very old and flawed approach to figuring out a step of predictors that is going to be good. Not systematic
Example:
Variable Rxy (validities)
Age .17
Gender .25
Education .09
Training .37
Motivation .03
Conscientious .28
Training would go in first since it has the highest correlation, then compute all partial correlations. Based off the partial correlations, the highest correlation is then selected and so on… |
|
|
Term
| Define Hierarchical Regression |
|
Definition
look at gain in prediction from adding additional predictors. Systematic buildup of an argument.
Example:
• Yhat = b1(age) + b2(gender) + b0
• Yhat = b1(age) + b2(gender) + b3(education) + b4(training) + b0
• Yhat = b1(age) + b2(gender) + b3(education) + b4(training) + b5(motivation) + b6(conscientiousness) + b0 |
|
|
Term
| Suppose you have a categorical variable with four groups, e.g. four regions of the country. You wish to use it as a predictor in a regression analysis. What is the general strategy for employing a categorical variable as a predictor in a regression analysis. |
|
Definition
| • Create a set of covariables and use the coveriables in the regression analysis so that you are not implying any order. |
|
|
Term
| In any coding scheme for g groups, how many codes are required to characterize the g groups? |
|
Definition
|
|
Term
| A dummy variable coding scheme with group 3 as the baseline group |
|
Definition
G D1 D2
1 1 0
2 0 1
3 0 0
YHAT = B1d1 + B2D2 + B0 |
|
|
Term
| an unweighted effects coding scheme with group 3 as the baseline group; |
|
Definition
G UE1 UE2
1 1 0
2 0 1
3 -1 -1
YHAT = B1UE1 + B2UE2 + B0 |
|
|
Term
| a series of orthogonal contrast codes. For example, be able to code these contrasts: contrast code that contrasts the mean of the first group with the average of the means of the second and third groups; a contrast code that contrasts the mean of the second group with the mean of the third group. |
|
Definition
G C1 C2
1 2 0
2 -1 1
3 -1 -1 |
|
|
Term
For dummy coding, be able to take the general regression equation and the codes and explain what each of the coefficients in the equation is measuring
Example: YHAT = b1D1 + b2D2 + b0 |
|
Definition
B0 = the mean of the base group
B1 = the difference between (the mean of group 1) – (the mean of group 3 [base group])
B2 = the difference between (the mean of group 2) – (the mean of group 3 [base group]) |
|
|
Term
| Are dummy codes centered? |
|
Definition
|
|
Term
| Are the pairs of dummy codes in a dummy variable coding scheme orthogonal? |
|
Definition
|
|
Term
| What sort of data configuration lends itself to coding with dummy codes? |
|
Definition
| A definite control group and a definite base group |
|
|
Term
| Suppose you run a one factor analysis of variance on a data set like that in the DATA LAYOUT above, q.6 (three groups). What will be the relationship of the resulting ANOV summary table to a regression analysis in which a set of dummy codes are used to code the three groups, and the criterion is the same as the dependent variable in the regression analysis? Explain the relationship of hypothesis for the overall F test in ANOV and the F test from this corresponding regression analysis. (Handout 10, page 5). |
|
Definition
ANOVA AND REGRESSION TABLE ARE EXACTLY THE SAME
Regression Anova
Ss regression Ss between
SS residual SS within
Df Df (same)
H0 = p2Y1d1d2 Ho = M1 = M2 = M3
null hypothesis for regression:
Group members has no relationship to the criterion in both hypothesis |
|
|
Term
For unweighted effects coding, be able to take the general regression equation and the codes and explain what each of the coefficients in the equation is measuring if the groups are of equal size (see Handout 10, page 8). Be able to show how to find the deviation of the baseline group from the grand mean when unweighted effects codes are applied in the equal group case.
Example: YHAT = b1UE1 + b2UE2 + b0 |
|
Definition
B0 = the unweighted grand mean (4 + 8 + 6) / 3 = 6
B1 = the difference between (the mean of group 1) – (the grand mean)
B2 = the difference between (the mean of group 2) – (the mean of group 3 [base group])
o Example:
• GR1 = MEAN 4 ; GR2 = MEAN 8 ; GR3 = MEAN 6
• B0 = 6
• B1 = 4 – 6 = 2
• B2 = 8 – 6 = 2
Group 3 – the grand mean = -(b1 + b2) = -(-2 + 2) |
|
|
Term
| How does the ANOV summary table for the data in the DATA LAYOUT relate to the analysis of regression summary table when the groups are coded with a set of unweighted effects codes? |
|
Definition
| Identical in every respect |
|
|
Term
| Are unweighted effects codes centered for equal group size? for unequal group size? |
|
Definition
Are centered for equal sample size
Not centered for unequal sample size |
|
|
Term
| Are unweighted effects codes orthogonal? |
|
Definition
|
|
Term
Consider gender as a dummy coded varaible, 1=male, 0=female. Suppose you have the coefficients for the overall regression equation, where X is continuous and D is a dummy code
Yhat = .4X + .3 D + .2XD + 1.5
Explain what each of the four coefficients (including the intercept) measure. |
|
Definition
|
|
Term
Write the simple regression equation:
Yhat = .4X + .3 D + .2XD + 1.5 |
|
Definition
Yhat = .4X + 1.5
note: B1X & b0 only apply to the group coded 0 (females) |
|
|
Term
| How would you get a simple regression for the group coded one (males) |
|
Definition
| The easiest thing would be to reverse the codes, so that 1=female, 0=male, and rerun the regression equation. |
|
|
Term
| What is a design matrix? What does it contain? |
|
Definition
A design matrix is a set of UE Codes
It captures all the effects in a design, all the factors and their interactions. |
|
|
Term
| In a design matrix, what is the relationship of the degrees of freedom for the ANOV summary table and the number of effect codes. |
|
Definition
they are both the same
Each code has 1 degree of freedom. |
|
|
Term
| What does it mean to say that with effects codes, the ANOVA partitions of variation are orthogonal? |
|
Definition
| The variation is not overlapping |
|
|
Term
| Now suppose you have unequal n's. Are the partitions of variation still orthogonal |
|
Definition
|
|
Term
| What is Type III partialing in SAS GLM, in SPSS GLM? Regression or "unique" partialing in SPSS MANOVA? |
|
Definition
| Each effect with all other effects partialed out |
|
|
Term
| Show the regression equation for a two-group experiment with a continuous variable included. In the analysis of covariance, what is the categorical variable called? the continuous control variables? |
|
Definition
| ANCOVA: YHAT = B1X [covariate] + b2C [categorical] + b0 |
|
|
Term
| Show the difference in the data configuration for ANCOVA in a true experiment versus in a quasi-experiment. Why is there no correlation between the covariate and the variate in the true experiment? With what two things can the covariate be correlated in a quasi-experiment with nonrandom assignment? |
|
Definition
• In true experiment, categorical variable of treatment is randomly assigned. No correlation between X and C
o X [Y] C (X and C are independent while overlapping with Y)
o X = math ability of parent; Y = math achievement ; C = random treatment
o Partial out individual difference with math ability based on parent ability. Gives more power because it partials out X and leaves [Y] and C overlap with the X taken out.
• Quasi-experiment, non-random assignment so that the treatment group membership can relate to the covariate
o XC[Y] (all are overlapping circles)
o X = math ability; Y = math achievement ; C = non-randomized treatment
o School by intel facility example |
|
|
Term
| What is a within class regression line in the ANCOVA? What assumption is made about within class regression lines in analysis of covariance? If the assumption is met, is the treatment effect constant over all levels of the covariate? |
|
Definition
Take the covariate (parent math ability) with criterion (child math achievement) and plot the regression of online group, within class regression. Plot the regression of the classroom group, within class regression.
Assumption: Slope is homogeneous
The treatment effect is constant |
|
|
Term
| If the covariate (continuous variable) interacts with the categorical variable in ANCOVA, what does this tell you about the slopes of the within class regression lines in the groups of the ANCOVA? What is the difficulty in coming up with an estimate of the treatment effect in ANCOVA if the covariate interacts with the categorical treatment variable? |
|
Definition
| Not equal (lines not parallel, interaction between the covariate X and the treatment C). Treatment effect is conditional on the covariate. |
|
|
Term
| Write a regression equation for a categorical predictor "C", a continuous predictor "X", and their interaction. Rearrange this equation into the simple regression equation for the regression of Y on X at values of the categorical variable C. |
|
Definition
1. Yhat = b1X + b2C + b3XC + b0
2. Yhat = (b1 + b3C)X [simple slope] + (b2C + b0) [simple intercept] |
|
|
Term
| What is meant by a fixed effects regression model? Under what condition will all inferences be correct in a fixed effects multiple regression, even if we merely sample cases and observe both X and Y? |
|
Definition
1: all the predictors are measured without error. 2: they take on a fix range of values (i.e. we take 1 year olds, two year olds, etc… not a continuum).
If we have multivariate normality of all variables, what that does gives us normally distributed residuals. We are find to inference, as long as we have normally distributed data. |
|
|
