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### 60 Cards in this Set

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 regression predicts what? causation corelation shows what? association, which is not causation Regression formulas SST(total sum of squares) =? SSR + SSE= sum of (y-y bar) squared Regression sum of squares S=sum of all vertical deviations from proposed line squared S=e1^2+e2^2+e3^2 Regression the best straight line, is one that ? minimizes S smallest S is the best line A least squares regression selects line with? the lowest sum of squared errors Regression The coefficient of determination is? the higher its value the more? R^2 higher value=more accurate R^2 measures what? relationship btween INDV and DV Regression Standard Error equation Square root (SSE/ N-K N=# obs in sample K=number of INDV Regression Interpolation prediction using value of IDV within observed range uncontroversial Regression Extrapolation preduction using value of IDV outside observed range should be avoided, if poss Simple Linear Regression IDV AKA DV AKA idv=predictive variable dv=response variable 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 in simple linear regression R^2=? r^2 r-correlation coeffienct R^2-coefficient of determination Multiple Linear Regression E= B0. B1, Bn = statistics error in population residual in sample B's=unkown parameters 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 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 forward multiple regression pick IDV that explains most variation in DV, then the next one-1 at time, till no variables significant explain variation mixed of backwards and forward do forward selection first, but drop variables which become no longer significant after introduction of new variables not used much 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 Assumptions for Multiple Linear Regresions -normal distribution -variance of regression line is same for all values of explanatory variables -explanatory variables (IDV) are not correlated Nonlinear functions can be fit as? regressions -logarithmic, exponential what is multicollinearity problem in interpretation of regression coefficients when IDV are correlated what is collinearity exists when IDV are correlated detecting multicollinearity chekin correlation coefficient matrix Ftest sig with many insig t VIF>5 what is VIF variance inflation factor quantifies sverity of multicollinearity in ordinary least squares regression gives variance of an estimated regression coefficient is increased cuz of collinearity how to correct for multicollinearity 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 what is adjusted R^2 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 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 Logistic transformation 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) types of logistic regression simple multiple multinominal 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 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 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 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 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 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) 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 example of parametric stats peasrson correlation coefficient(r) unpaired/paired t test ANOVA Regression Non parametric stats assumptions? distribution-free stats second class of inferential stats usually nominal or ordinal but CAN be continuous(nom + ratio) nonparametric stats examples? chi-square sign test fisher exact test sign test define test the equality of median of 2 comparative groups simplest nonparametric test used for quick look at data for parametric 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 chi square stats define nonparametric test to c if relatinship exists btwn caregorical variables gender, ins type, statisfaction chi square tests? "goodness of fit" btwn observation and theorretical distribution values of 0 to infinity chi square hypothesis H0-data follow specified distribution Ha: does not follow 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 Chi Square fe= (fr*fc)/N r=row, c=column N=# of subjects df= (C-1)*(R-1) main diff in descriptive and inferential stats? inferential has hypothesis testing define correlation interrelationship btwn 2 CONTINUOUS variables-interval and ratio Assumptions of correlation 1-normality-normal distribution 2-Linearity-linear relationship 3-homoscedascity-err or residual variance in model are identically distributed what statistic to test homoscedascity? F-test correlation coefficient what does it indicate ranges from? r -direction + strength of correlation -1.0 to 1.0 pearson correlation refers to spearman correlation refers to simply correlation(continuous variable) spear-alternative for pearson, continous varibale but not normal distribution(nonparametric) what is type 3 error correctly reject Null, for wrong reason 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 correlation how to calc df degrees of freedom is N-2***************** factors that influence the correlation 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 correlation CANNOT be equated with? causation correlation co-efficient ranges 0-.2 very low .2-.4 low .4-.6 mod .6-.8 highly mod .8-1 very high