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Study Guide Exam 1
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- 1What is the phi correlation?if we have 2 categorical variables (training and gender), the correlation between the 2 categories (the 2 dichotomies) is the phi coefficient. Phi is pearson product correlation. if we have 2 categorical variables (training and gender),
- 2What is the point biserial correlation?correlation between one true dichotomy and one continuous variable (training, past experience). Ex: Corrleation between days absent and treatment condition.
- 3Give examples of how a correlational study and an experimental study could be handled in regression analysis, and of the control of person variables in the analysis of an experimental manipulationCorrelational: predict job performance based on b1 (past experience in years). observational study.
Experimental: predict job performance based on past experience (b1) and training condition (b2). Manipulation. Dummy Codes can be assigned to any experimental condition. - 4How can I test whether treatment condition predicts scores on the dependent variable in a regression analysis?Use experimental design to predict job performance based on training condition (coded 1) or not (control, coded 0). Use F test for overall significance of prediction. Null: rho = 0.
- 5What is the relationship of the overall F test for prediction in the regression analysis and the overall F test for the Condition (Experimental versus Control) in the ANOVA?The F-test is structured the same, the math/calculations are the same. Run as ANOVA F-test, null: mean in training equals mean of control. Run as ANOReg F-test: tests the significance of prediction of the dependent variable from the predictor.
- 6Explain three uses of multiple regression: description, prediction, and explanation and theory testingDESCRIPTION: Summarize relationships within the regression equation.
PREDICTION: use regression equation to predict future outcomes from currently or previously gathered data. -epidemiology
THEORY TESTING: specifying a regression equation that operationalizes a model or theory and testing whether specific regression coefficients corresponding to hypothesized relationships are significant or not. - 7What three criteria must be met for making causal statements about the relationship of X to Y?1) relationship between X and Y (between cause and effect), needs to be a correlation between the two.
2) temporal precedence: the cause should precede the effect. Cross sectional data uses causal language.
3) no spurious relationship: an omitted third variable that is producing the relationship between X and Y. random assignment is what eliminates spurious relationships. - 8what is a true dichotomy?Refers to a discrete categories, a true category, (political party, gender).Gender is a true dichotomy.
- 9The measure of central tendency is the ___. The measures of variability are ___, ___, and ____. The measures of relationship are ____,____, and ____.-Arithmetic Mean
-Variation, Variance,Standard Deviation
-Covariation, Covariance, Correlation - 10What is an artificial dichotomy?Refers to categories produced by a cut score on a continuum. Ex: pass vs. fail based on some continuous test score.
- 11Can you calculate the Phi coefficient between two true dichotomies and the point-serial correlation between a true dichotomy and a continuous variable using standard software for the Pearson product moment correlation?yes
- 12Are the phi and point-biserial correlations actually Pearson product moment correlations ?yes
- 13What does the notation in the subscript of byx signify?-summarizes relationship of the predictor to the criterion
-prediction of Y from X
-coefficient for the regression of Y on X - 14What is the function of the regression intercept, b0 ?-Y -intercept
-Value of Y when X=0
-makes the mean of the predicted scores (Ybar hat) = the mean of the observed criterion scores (Y bar) - 15If there is no relationship between predictor X and criterion Y, what is the best prediction of Y for any value of X?The mean of Y
- 16Into what two components can we partition any observed criterion score? What does each of these components measure?1) Predicted score- systematic prediction from the equation
2) Residual score-part we fail to predict.
Allows us to take the total variation of Y, the variation of the observed criterion score and break it into the variation of the predicted scores (SS yhat) and the variation of the residual scores (SSy-yhat) - 17What does r squared yyhat measure? what is it called?-measure of overall effect size for the whole regression analysis
-measures the proportion of variation in the criterion accounted for by the set of predictors.
-called r squared multiple, squared multiple correlation.
--one of these measures per equation. - 18When The variation of predicted scores equals the variation of observed scores, we have....Perfect prediction: SSyhat= SSy
- 19Are the Predicted Scores and Residual Scores orthogonal or do they share overlapping variance?orthogonal. no overlapping variance.
- 20In general, what hypothesis is tested in the analysis of regression?tests the significance of the proportion of the observed criterion accounted for by the predicted values in the population.
H0: rho^2 yyhat=0
H1: rho^2 yyhat > 0
null hypothesis states that in the population the proportion of variation accounted for by the predictor is equal to zero. . expressed in terms of squared multiple correlation -rho squared yyhat- between Y and Yhat in the population. - 21What is the structure of the F test and its degrees of freedom in the one-predictor case?MSregression divided by MS residual. Numerator: systematic predictable variation + random error.
Denominator: random error.
df regression= 1
df residual= n-2
df total= n-1 - 22In general, if you reject the null hypothesis in ANOReg, what does this mean?we have accounted for a significant proportion of variation in the criterion Y with our predictor X. If we did not have a regression equation, our best guess would be the mean of Y. Using our equation to predict Y gives us more accurate prediction of Y than just chance guessing.
- 23What are meant by biased versus unbiased estimators?Biased: Expected value of the sample stat is different than (greater than or less than) the corresponding population parameter.
Unbiased: one whose expected value equals the corresponding population parameter. Sample mean is unbiased estimator of population mean. - 24What is a sampling distribution? How would you create a sampling distribution of a regression coefficient? Is the sample regression coefficient an unbiased statistic or a biased statistic?-relative frequency distribution of a sample statistic
-drawing samples over and over again
-unbiased stat. - 25What is the standard error, what does it measure?a
- 26what 2 things can we do to decrease the standard error of the regression coefficient?b
- 27what hypothesis is tested in testing the significance on an individual regression coefficient?b
- 28if you reject the null hypothesis on an individual regression coefficient, what does this mean? can you say that the predictor whose regression coefficient is significant CAUSES the criterion?c
- 29what is the standard error of estimate?d
- 30what is the general structure of all confidence intervals?e
- 31what 2 values are contained in the allowance factor? what is another name for the allowance factor?e
- 32If a confidence interval on a regression coefficient includes the value zero, what does that tell you about the significance of the regression coefficient?20
- 33Provide an interpretation for the following confidence interval: C[.46 <_ Beta yx<_.79]=.9920
- 34explain what unstandardized b yx measuresthe change in the criterion Y for a one unit increase in the predictor
- 35in what units are standardized regression coefficients measured?standard deviations
- 36A) if an unstandardized regression coefficient = .7, what does this mean? B) If a standardized regression coeffience =.7, what does this mean?A)
- 37In general, what is meant by a "loss" function? Explain in words what is being minimized in the regression model we are studying.24
- 38What is the loss function called for regression analysis?the least squares criterion
- 39State the 4 steps involved in an ordinary least squares solution1)
2)
3)
4) - 40what does the first derivative of the loss function measure? Why do we set this derivative equal to zero?25
- 41What are normal equations?25
- 42what is the difference between pairwise and listwise deletion? explain how each treats missing data. are they approaches the current state of the art or are there newer approaches?26
- 43what is a scatterplot matrix? what is contained in a scatterplot matrix? How is it laid out?27
- 44what does the kernel density plot portray about a univariate distribution?28
- 45what is a lowess line? Is a specific model involved in generating the line? What does it show us in a bivariate plot?29
- 46What does a lowess line show us in a bivariate plot? How is it affected by extreme scores at the ends of the continuum? How does the percent of points involved in smoothing affect the appearance of the lowess line?29
- 47what is a box and whiskers plot? What does it show? What does the box show? What does the heavy horizontal line in the box show? What do the long vertical lines illustrate?-compares the distribution of a variable across groups, and to display the distribution of a variable in a single group.
-data broken up into quartiles
-rectangular box illustrates the middle 50% scores
-heavy horizontal line within the box is the median on the variable.
-vertical lines going upward and downward from the box represent the range of the scores beyond the middle 50% of scores - 48Describe the structure of all t tests31
- 49if you test the unstandardized regression coefficient for significance with a t-test, and then you test the standardized regression coefficient for significance with a t-test, how do the values of the 2 t-tests relate to one another? what are the degrees of freedom of each t-test?32
- 50What is estimation in statistics? What are point estimates? What are interval estimates?estimation is using value of sample stats to make “informed guesses” about the value of corresponding population parameters.
- point: one to one estimate from sample to population based on sample mean
-interval: takes value in sample and estimates a RANGE of values within which parameter might lay - 51What is the criterion for the solution to the regression coefficient(s) and regression intercept in OLS regression?Ordinary Least Squares criterion
- 52Explain how correlation coefficients are affected by the distribution of the variables being correlated. Under what condition will the maximum possible correlation not reach r=1.00 or r= -1.00?-only if the distribution of the 2 variables is identical. If there is a skewed score, the correlation will not be 1.
- 53What is the effect of unreliability in variables on the correlation between the variables?-unreliability: measure with same test but don’t get same score, due to error in the measurement
-what this does to correlation coefficients, attenuates the correlation (brings it closer to zero). Ex: correlation =.6, unreliable will make it .3. makes test weaker. - 54What is restriction of range? How, if at all, does restriction of range affect the correlation between two variables?-restriction of range: small range on x or y. also attenuates correlation coefficients.
-scores on GRE are good example: doesn’t predict. Narrow range at top is not predictive, GRE is designed to separate those who can go to grad school and those who cannot. - 55Suppose the correlation between child IQ and reading level is equal to .35 in the second grade in a general elementary school class serving the whole school. In a gifted class of high IQ children, the correlation is .09. What is a possible source of the difference in correlation between the two classrooms?restriction of range
- 56What two components comprise an observed score in true score theory? Using these components, define the reliability of a score in terms of true score theory.-observed score = true score + error
-assumed to be orthogonal
-observed variance = true score variance + error variance
reliability: rhoxx in population (rxx in sample) = true variance/observed variance → reliability is the proportion of all variance in a score that is true score variance and is available to correlate with other scores - 57How does restriction of range affect unstandardized regression coefficients? Standardized regression coefficients?-correlation is attenuated by restriction of range, and standardized regression coefficients are based on correlations, so standardized regression coefficients are attenuated by restriction of range.
-unstandardized regression coefficients are NOT AFFECTED by restriction of range
-see pages from book 53-57 - 58what is 1 of 2 indices by which we can compare groups in terms of relationships between variables? what question does it answer? how is it affected by restriction of range and unreliability?-byx the unstandardized regression coefficient compared across groups, answers the question of whether a one unit increase in X is associated with a constant change in Y.
-unaffected by restriction of range in the predictor X
-attenuated by unreliability in X - 59what is the 2nd index by which we compare groups in terms of relationships between variables? What question does it answer?-rxy, the pearson product moment correlation, answers the question of whether one variable accounts for the same proportion of variance in another variable in the 2 groups.
-to the extent that the X and/or Y variables have different reliabilities or different ranges across groups, the value of rxy will differ across groups. - 60What are part-whole correlations? Can we use standard significance tests for testing the significance of part-whole correlations?43
- 61What is meant by the Fixed Effects Regression Model?It is the model underlying OLS regression.
-assumes that predictors are measured without error (perfect reliability) and that the predictors take on a fixed set of values. - 62what does by1.2 and by2.1 signify? Why are these coefficients called "partial regression coefficients?-regression of x on y while holding x2 constant
called partial regression coefficients because we are taking the part of one predictor that’s independent (the sliver that’s left) and seeing how its correlated with y - 63In a 2-predictor regression analysis, describe how one would go about creating a score on predictor X2, that was completely indpendent of X1. Describe the 2 steps involved.first, predict X2 from X1. How much of X2 can you predict from X1.
-second, find the residual: X2-Xhat2 - 64Explain what is meant by "statistically controlling" or "partialing out" or "holding constant" a variable.-taking the unique part of the prediction that isn't shared with other variables
-taking into account any overlap and not including it - 65what is contained in the data matrix?noted X
columns: X1, X2, Y
Rows: elements/subject #
Within the matrix: individual scores - 66what is contained in the covariation matrix?noted P
columns: X1, X2, Y
Rows: same as columns
Main diagonal: variation of X1, X2, and Y
Off the main diagonal: covariation between each pair of variables - 67what is contained in the covariance matrix?noted S
Rows & columns: x1, x2, y
main diagonal: variance of each predictor and the criterion
off the main diagonal: covariance
*computed by dividing every element in the covariation matrix by (n-1)* - 68what is contained in the correlation matrix?noted r
columns and rows: x1, x2, y
main diagonal: 1.00 (correlation of each variable with itself.
off the main diagonal: correlations between variables
validity vector: column of correlations of each predictor with the criterion - 69How, if at all, do the steps involved in the least squares solution for the two-predictor case differ from the solution in the one-predictor case?Does not differ at all, regardless of # of predictors
- 70Under what condition, if any, will the unstandardized regression coefficient for predictor X1 in the two predictor regression equation, equal the unstandardized regression coefficient for X1 in the one predictor case? What about the standardized regression coefficient for X1 in the one predictor versus the two predictor case?under the condition that the 2 predictors are completely uncorrelated, that is to say that they share nothing in common.
same is true for standardized regression coefficients. - 71Explain the squared multiple correlation in terms of the observed criterion score and the predicted score.It is the correlation between the observed and predicted scores.
Answers the question: does the predicted score actually correlate with the actual score?
-overall effect size measure, measures accuracy of our prediction. - 72What is a linear combination?any score that is comprised of other scores in the form of: a1x1+a2x2...+bpxp+b0
-predicted score, yhat, is a linear combination of predictors - 73If you use other than OLS weights in computing the predicted score, can you obtain a higher correlation between Y and than with the OLS weights?no, the weights are specific for maximizing correlation
-page 17 handout 3 - 74Under what circumstance will the squared multiple correlation equal the sum of squared validities?only if the predictors are completely uncorrelated
- 75how does the number of predictors affect the size of the standard error for each predictormore predictors, larger standard error
- 76how is R2multiple is built into standard error? how does R2multiple affects the size of the standard error for each predictor?(1-r squared 12) is the proportion of one predictor that is independent of the other predictor.
larger r squared multiple, smaller standard error - 77the higher the correlation between predictors...the larger the standard error
- 78what is r squared sub 12?correlation between predictors: proportion of variation in one predictor that is redundant with the other predictor
- 79what is (1-r squared sub 12) ?Tolerance: proportion of one predictor that is independent of the other predictor.
-proportion of non-overlap - 80what does a tolerance of 1 mean?you have uncorrelated predictors, completely independdent of each other
- 81what is VIF?variance inflation factor: indicates by how much the squared standard error of regression coefficients is inflated due to correlation between predicotrs.
reciprocal of Tolerance: 1/(1-r squared sub 12) - 82bigger tolerance means...lower standard error
- 83bigger VIF means...higher standard error
- 84how do the number of predictors and sample size affect shrinkage?more predictors-> more shrinkage
larger sample size--> less shrinkage - 85What is contained in the covariance matrix of the regression coefficients?rows and columns are regression coefficiencts.
the variance of each regression coefficient (square of the standard error), and it gives the covariance between pairs of regression coefficients. - 86Conceptually explain how you could compute the covariance between two regression coefficients based on repeated samples from the same populationcompute the raw regression equation in each sample, this determines how much our estimate of regression coefficients varied across samples drawn from the same population. We would end up with a series of estimates of each regression coefficient. The series of estimates becomes our data set in which each data point is an estimate of a regression coefficient.
- 87How would you compute the standard errors of regression coefficients from the covariance matrix of the predictors?take the square root of variance, this is standard deviation of the regression coefficient which is the standard error
- 88what does an overlay plot show?shows 2 or more dependent variables as a function of a single independent variable
- 89what is meant by "linear trend has been removed" ? why is the slope zero?When we plot the residuals as a function of predictor X, we no longer see the linear trend. the linear relationship between x and y has been removed.
-slope =0 because there is no linear trend between the residuals as a function of X
-no relationship of the predictor score to the residual - 90what is standard error of estimate?-standard deviation of residual scores, used in computing the z-score of the residuals
-square root of MSresidual
-root MSE - 91why do we use adjusted r square multiple?we want to adjust for the positive bias in r square multiple
-takes into account the number of predictors and sample size
-creates a more accurate assesment in our population
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- 01 Multiple Regression Fichas sobre Study Guide Exam 1, creado por Molly Gardner7797 el 16/02/2016.
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