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60 Cards in this Set
- Front
- Back
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regression predicts what?
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causation
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corelation shows what?
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association, which is not causation
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Regression formulas
SST(total sum of squares) =? |
SSR + SSE= sum of (y-y bar) squared
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Regression
sum of squares |
S=sum of all vertical deviations from proposed line squared
S=e1^2+e2^2+e3^2 |
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Regression
the best straight line, is one that ? |
minimizes S
smallest S is the best line |
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A least squares regression selects line with?
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the lowest sum of squared errors
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Regression
The coefficient of determination is? the higher its value the more? |
R^2
higher value=more accurate |
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R^2 measures what?
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relationship btween INDV and DV
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Regression
Standard Error equation |
Square root (SSE/ N-K
N=# obs in sample K=number of INDV |
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Regression
Interpolation |
prediction using value of IDV within observed range
uncontroversial |
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Regression
Extrapolation |
preduction using value of IDV outside observed range
should be avoided, if poss |
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Simple Linear Regression
IDV AKA DV AKA |
idv=predictive variable
dv=response variable |
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Sig Testings in Regression
explain the diff tests involved |
F-tes= judges if explanatory variable(indep), adequately describe outcome variable
T-test= applies to indivd. IDV(explanatory)-says if this particular variable has effect on outcome,holding others same R^2-measures strength of relationship of IDV and DV |
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in simple linear regression
R^2=? |
r^2
r-correlation coeffienct R^2-coefficient of determination |
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Multiple Linear Regression
E= B0. B1, Bn = |
statistics error in population
residual in sample B's=unkown parameters |
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Multiple Regression
3 ways to do it, what are they? |
1)Backward multiple regression
2)Forward multiple regression 3)Mix of back/forward multiple regression |
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backward multiple regression
AKA? How to do it? how to evaluate individual relationship |
AKA reverse elimination
drop least sig variables one at time, til left with only sig variables t test evaluates the inividual relationship |
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forward multiple regression
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pick IDV that explains most variation in DV, then the next one-1 at time, till no variables significant explain variation
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mixed of backwards and forward
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do forward selection first, but drop variables which become no longer significant after introduction of new variables
not used much |
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Multiple Regression
Dummy Variable aka? what does it do? |
indicator variable
introduces qualitative -gives values of 0 or 1 to indicate absence of prescence of caregorical info female= 1 when pt is female female=0 when pt is male |
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Assumptions for Multiple Linear Regresions
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-normal distribution
-variance of regression line is same for all values of explanatory variables -explanatory variables (IDV) are not correlated |
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Nonlinear functions can be fit as?
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regressions
-logarithmic, exponential |
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what is multicollinearity
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problem in interpretation of regression coefficients when IDV are correlated
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what is collinearity
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exists when IDV are correlated
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detecting multicollinearity
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chekin correlation coefficient matrix
Ftest sig with many insig t VIF>5 |
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what is VIF
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variance inflation factor
quantifies sverity of multicollinearity in ordinary least squares regression gives variance of an estimated regression coefficient is increased cuz of collinearity |
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how to correct for multicollinearity
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pick IDV with low collinearity
use stepwise regression-where u put most correlated variable in equation 1st, then next most order of entry of variables matters here |
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what is adjusted R^2
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adjusts for inflation in R^2 caused by number of varibales in equation
as sample size increase >20 cases per variable, asjut is less needed basically go with asjusted R2 unless, sample size > IDV *20 |
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logistic regression
define AKA |
multivariate regression that uses max likelihood estimate to see relationship btwn CATEGORICAL dependent(Y) and multiple IDV(X)
AKA logit analysis |
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Logistic transformation
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event occurrence (NO, YES)
---> PROB (0.....1) ------->ODDS (0...+INF) do P/1-P for each value=odds then do log (o) and log (inf) = (-inf to + inf) |
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types of logistic regression
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simple
multiple multinominal |
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simple logistic regression
application DV ADV? |
relationship btwn single IDV(continuous or categorical) and single DV-usually binary variable
example: DV-yes/no IDV: yes/no |
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Multiple Logistic Regression
application DV: IDV |
relationship btwn 2 or > IDV (continuous of categorical) and single DV-usually binary
DV-Stroke(Yes/NO) IDV-age, HTN, diabetes, gender |
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Multinominal Logistic Regression
application IDV DV |
relationship btwn 2> IDV (cont or cat) and a single CATEGORICAL dv with more than 2 possible choices
DV-HTN(bad/mod/ok) IDV-age,race,meds,gender AKA polytomous logistic regression |
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define
Odds Odds ratio(OR) |
Odds-ratio of probability of success to prob of failure
=P/(1-P) Odds Ratio(OR)-ratio of adds an event occur in one group to odds of others OR=Oddsgrp1/Oddsgrp2 |
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What do each of these mean
OR=1 OR>1 OR<1 |
OR=1 no association
>1 positive association of grp1 and grp2 <1 negative assoc. of grp1 + grp2 |
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Relative Risk
define AKA |
prob that member of exposed grp will develop disease to prob member of unexp develops same disease
RR=P(Disexp)/P(Disunexp) |
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parametric stats
what class of stats? assumptions? |
its inferential
-normally distributed -estimation of at least 1 parameter -at least 1 interval measures mean=mode=median |
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example of parametric stats
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peasrson correlation coefficient(r)
unpaired/paired t test ANOVA Regression |
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Non parametric stats
assumptions? |
distribution-free stats
second class of inferential stats usually nominal or ordinal but CAN be continuous(nom + ratio) |
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nonparametric stats
examples? |
chi-square
sign test fisher exact test |
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sign test
define |
test the equality of median of 2 comparative groups
simplest nonparametric test used for quick look at data for parametric |
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Sign Test
data? assumption computation? |
paired data(DV)
assumption-each paired diff is meaningful comp-1-do diff of each paired data 2-discard any zeros 3-apply sign test 4- hypothesis testing |
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chi square stats
define |
nonparametric test to c if
relatinship exists btwn caregorical variables gender, ins type, statisfaction |
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chi square tests?
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"goodness of fit" btwn observation and theorretical distribution
values of 0 to infinity |
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chi square hypothesis
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H0-data follow specified distribution
Ha: does not follow |
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chi square
data? assumption? computation? |
DV-nominal or ordinal
assumption-data are indep random samples from population comp-conduct a R*C contringency table -compute expected value -do formula -hypothesis testing |
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Chi Square
fe= |
(fr*fc)/N
r=row, c=column N=# of subjects df= (C-1)*(R-1) |
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main diff in descriptive and inferential stats?
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inferential has hypothesis testing
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define correlation
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interrelationship btwn 2 CONTINUOUS variables-interval and ratio
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Assumptions of correlation
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1-normality-normal distribution
2-Linearity-linear relationship 3-homoscedascity-err or residual variance in model are identically distributed |
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what statistic to test homoscedascity?
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F-test
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correlation coefficient
what does it indicate ranges from? |
r
-direction + strength of correlation -1.0 to 1.0 |
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pearson correlation refers to
spearman correlation refers to |
simply correlation(continuous variable)
spear-alternative for pearson, continous varibale but not normal distribution(nonparametric) |
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what is type 3 error
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correctly reject Null, for wrong reason
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correlation
null hypothesis? alt? how to test |
H0-correlation between two is 0, uncorrelated
ha-is nonzero to test if r is sig diff from 0, we use t test for pearsons r |
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correlation
how to calc df |
degrees of freedom is N-2*****************
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factors that influence the correlation
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1-correlation coeff(2)..closer r is to -1 or +1 the greater chance of significance
2-sample size-larger samples, greater chance of sig 3-linearity-correlation only exists in linear relationship |
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correlation CANNOT be equated with?
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causation
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correlation co-efficient ranges
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0-.2 very low
.2-.4 low .4-.6 mod .6-.8 highly mod .8-1 very high |
