Multiple Regression Exam 1 Flashcards

Terms Definitions
What do you look at to determine what accounted for the most variance?
β or beta weight
This is the proportion of the total variance in the DV uniquely contributed by the IV.
Sr2 (semipartial squared)
What is the formula for a regression equation?
Y'(prime) = a + b1(X1) + b2(X2) + b3(X3) .... (and so on for however many variables you have)
Where can you find the constant for your regression equation?
Unstandardized coefficient column, (constant) in β row
Which type of beta (β) can be compared to one another?
Standardized beta (β)
What is the difference between univariate and multivariate statistics?
univariate - single DVmultivariate - multiple DVs
What is a Type I error?
When you reject the null hypothesis but should have in fact accepted it (or failed to reject it).
What is used to minimize the deviations between Y and Y'and used to optimize the correlation between Y and Y'?
β weight or unstandardized regression coefficient
What is multicollinearity?
the variables are highly correlated to one another
What is singularity?
the variables are redundant; one of the variables is a combination of two or more of the other variables
What do singular or redundant variables do to an analysis?
They weaken the analysis by inflating the size of the error term.
How do you correct for singularity?
Run your analysis. Typically the computer will balk (or abort the analysis). If the run aborts, delete the offending variable.
What is the difference between ANOVA and ANCOVA?
ANOVA - IV's are levels of discrete variables, one DVANCOVA - one DV, some IVs and a covariate
What type of beta weight do you want to use for interpretation? (when comparing one variable to others)
Standardized beta weights
What can regression tell us and what CAN'T it tell us?
It can tell us about correlations. It cannot attribute causality.
What does a significant r2 change in regression mean?
It tells us that the predictor was significant.
What might be problematic in relation to cases and IV's and their ratio?
The cases to IV ratio must be substantial. If you have more IVs than cases, it becomes an issue.
What are the different functions a covariate can have in an ANCOVA?
What does reducing the error term do?
It increases your chances of having an effect.
What is one's goal when picking covariates?
To maximize adjustment of DV while minimizing the loss of df for error
What is a bivariate correlation?
measure of association between two variables
What is a semipartial correlation?
estimate of the unique contribution of the IV to the total variance of the DV (contribution of the other variables is taken out of DV) * more useful than partial correlations
What is a partial correlation?
estimate of the unique contribution of the IV to the unexplained variance in DV; contribution of other variables is taken out of IV and DV
In a normal distribution, what do the skewness and kurtosis look like?
They are both zero.
What is the advantage to using MANOVA?
get to include multiple DVs
What are continuous variables?
-anything in the range of a scale-size of the number reflects the "amount" of the variable-interval or quantitative
What are dichotomous variables?
nominal, categorical, or qualitative
Treatment + Error____________________ = Error
What are the assumptions for an ANOVA?
1. Categorical IVs2. Normality3. Homogeneity of Variance4. Independence of Scores
What are some ways to correct for Type I Errors?
-Bonferroni adjustment-Scheffe (post -- most stringent in SPSS)-Tukey (planned or post hoc)-Dunnett (post hoc test)
When the research question is related to the DEGREE OF RELATIONSHIP AMONG VARIABLES what analysis would be appropriate?
bivariate correlation with 2 variablesregression - 1 variable to predict another
When the research question is related to the SIGNIFICANCE OF GROUP DIFFERENCES what analysis would be appropriate?
t-test (2 levels)ANOVA (more than 2 levels)
When the research question is related to the PREDICTION OF GROUP MEMBERSHIP what analysis would be appropriate?
-discriminant functional analysis (when IVs are continuous)-logistic regression(IVs and DVs flip - turning ANOVA on its head
When the research question is related to the STRUCTURE OF THE DATA what analysis would be appropriate?
-factor and principle components analysis-structural equation modeling (SEM)
When the research question is related to the TIME COURSE OF EVENTS what analysis would be appropriate?
-survival analysis-time series analysis (looking to see if there is an abrupt change when intervention is implemented)
What is "good" data?
accurate data that represents what really exists (data was entered exactly as it was on the survey/raw forms.)
What is "bad" data?
Inaccurate data. It doesn't represent what really exists.
What is "ugly" data?
Accurate and representative data that does not fit the assumptions of analytical procedures. (potentially the most frustrating kind)
5 things to watch for when screening the data
Accuracy, Representativeness, Missing data, Violations of Assumptions, Outliers
What is linearity?
Straight line relationships between pairs of variables.Check by examining residual plots or bivariate scatterplots.
What is multiple regression used for?
to predict the score on the DV from scores on several IVs
Which type of statistical analysis is helpful when trying to figure out which of many IVs would be most helpful to use? (to reduce a larger set of IVs to a smaller set)
Sequential R (hierarchical)
Which type of multiple regression decides which IVs to include by data based decisions rather than decisions based on theory?
Stepwise (statistical)
What is a One-way ANCOVA designed to assess?
Group differences on a single DV after the effects of one or more covariates are statistically removed. (Covariates are chosen because of their known association with the DV)
Why would ANCOVA be used with naturally occurring groups?
to adjust for differences among groups
What is a One-way MANOVA designed to assess?
it is used to evaluate differences among composite means for a set of DVs when there are two or more levels of an IV group
What is a One-way MANCOVA?
more than one DV and covariates in the analysis; use covariates as pretests of the DVs.
What is a discrete variable?
these variables take on a finite and usually small number of values. There is no smooth transition from one value or category to the next. continents, categories, type of community
What is a continuous variable?
measured on a scale that changes values smoothly rather than in steps. These take on value within the range of the scale, and the size of the number of the scale itself. annual income, age, temperature, distances, GPA
Which analyses evaluate structure of the data?
factor and principal components analyses, structural equation modeling (SEM)
How can you check accuracy of the data?
Look at data; Check descriptive statistics(Mean, range, minimum, maximum, sd, count); Know the people who entered the data
When dealing with missing data what percent (if random) is not a great concern? What will be a concern if the missing data is nonrandom?
5% or less; generalizability of the results will be a concern
If the missing data looks like a nonrandom pattern, what can you do with missing cases?
delete cases, delete variables, or replace missing value
If you are deleting cases what two ways can you do it?
pairwise: deleting case from all analyseslistwise: deleting cases from analysese which involve the data point that case is missing
If missing data looks like a nonrandom pattern, what should you do?
try to preserve all data and try to explain the pattern.
How can you test for outliers with multivariate analyses?
Mahalanobis distance or leverage
What is Type II Error?
failing to reject the null hypothesis when in fact it should have been rejected
When does mediation occur?
when a variable accounts for the effect of a predictor on an outcome; the reason why the predictor affects the outcome
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