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73 Cards in this Set
- Front
- Back
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What is the range of possible values for r? |
-1 to1 |
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What part of r indicates the direction of theassociation? |
The sign of r |
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What part of r indicates the strength of theassociation? |
The magnitude (or absolute value) |
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What is r a proportion of? |
Theabsolute value of r is a proportion of maximum covariance between the 2variables |
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What type of association does r capture? |
Linear association |
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What typically happens to r when the range ofone of the variables is restricted? |
r is smaller than if we had the full range of variables |
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What is a point biserial? |
Pointbiserial is a correlation when one variable is dichotomous and the other iscontinuous. |
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What is the biserial? |
Biserialestimates what the correlation between the two variables would be if thedichotomous variable were the result of splitting a continuous normal variable.Underlying continuing distribution under the dichotomous variable. |
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If both point biserial and biserialcorrelations are calculated for the same variables, which correlation will belarger (in magnitude)? |
Biserial will be larger because the dichotomous variable assumed to be continuous will have greater variance. |
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What is phi? |
Use φ when both variables are dichotomous |
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What is tetrachoric? |
the tetrachoric estimates what the correlationbetween the two variables would be if both variables were the result ofsplitting a continuous normal variable (when there is an underlying continuousdistribution). |
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If both phi and the tetrachoric correlationare calculated for the same variables, which correlation will be larger (inmagnitude)? |
Thetetrachoric correlation will be greater in magnitude than phi because theassumed normally distributed underlying variable will have more variance tocorrelate with the other variable. |
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What criterion does least squares minimize? |
- Leastsquares picks the line that minimizes the sum of the squared deviations fromthe line.
- Sumof Squared residuals |
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Where do predicted scores fall? |
Onthe regression line |
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What is a residual? |
Differencesbetween actual and predicted Y scores (Y − Yhat) are called residuals. |
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What information does the intercept (Bsub0)give? |
Predictedvalue of Y at X=0 |
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What information does the slope (Bsub1)give? |
Changein Y for a 1 unit change in X |
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How does the sign of B1 relate tothe sign of r? |
Itwill be the same sign |
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Over what range of X values does theregression equation apply? |
Rangeused to estimate the model (the best fitting regression coefficient) |
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What is centering? |
Centering X means moving its zero point to a valuethat is interesting or meaningful |
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Why do we center? |
Whenx is centered, the intercept will tell the predicted y value at a point we careabout |
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When we center, which variable (X or Y orboth) is centered? |
Only X, NEVER Y!!! |
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Does the slope change when we center? |
No |
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Does the intercept change when we center? |
Yes |
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What is R2 the squared correlationbetween (by definition)? |
Squaredcorrelation between predicted and observed scores |
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In one-predictor regression only, R2is also the square of what correlation? |
Thesquare of RYY = rXY. Squareof the 0 order correlation between two variables |
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What is R2 a proportion of? |
Ittells the proportion of the variance in Y accounted for by the regression linebased on the association between X and Y. |
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How does the variance of Y hat (predicted scores) compare to thevariance of Y( observed scores)? Isit greater than, less than, or equal to? |
Y hathas no variance that is unrelated to Y. Y hatjust has less variance than Y. |
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In one-predictor regression only, what is therelationship between the values of the F test of R2 and the t-testof B1? |
The Ftest of R2 tests whether a set of predictors together predictvariance in Y. Thet-test of B1 tests whether a single predictor predicts variance in Y. |
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In one-predictor regression only, what is the relationship between their p-values? |
Whenthere is only one predictor, these tests are equivalent. They give the samep-value. |
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What does the standard error of estimate tell? |
Averageresidual deviation from the regression line or How farobserved Y scores deviate from the regression line |
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How you do find the SEM? |
Like the standard deviation, it is found bysquaring deviations, taking the average, and then taking the square root. |
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What does a confidence interval for B1tell? |
Range of values in which we believe the truepopulation variables fall. |
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How can the confidence interval for B1be used to perform a null hypothesis test for B1? |
Ifthe confidence interval includes zero, H0: θ1 = 0 is not rejected. Ifthe confidence interval does not include zero, H0: θ1 = 0 is rejected. -- it will be significant |
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How will results of this test compare to resultsfor the t-test of B1? |
Theresults will always be consistent/identical with the t-test because both usethe same SEB1. |
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What information does the intercept (B0)give? |
Valueof Y predicted when all predictors equal 0 |
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What information does each coefficient (B1... Bk) give? |
Partial relationship between predictors when partialling it out for other predictors. B1describes the association between X1 and Y, holding X2 constant (or partialingit out). B2describes the association between X2 and Y, holding X1 constant (or partiallingit out). |
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Under what circumstances could the F test of R^2be significant, but no predictors are individually significant? |
Whenthe predictors are highly correlated with each other. |
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When two (or more) predictors overlap invariance they account for in Y, to which predictor is the overlapping varianceaccounted for attributed to? |
Justgets discarded; doesn’t belong to either |
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What does R2 for predicting X1from all the other predictors (which appears in the denominator of the standarderror formula for B1) measure? |
Need Info |
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What is suppression? |
Whenthe sign completely flips when you add in another predictor |
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Why do we use standardized coefficients? |
Usingstandardized units circumvents the issue of having to ensure that readersunderstand something about the scale of variables being used. |
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How are standardized coefficients found?(Which variables—X’s or Y or both—are standardized?) |
- Tostandardize a variable, subtract the mean from each value and divide by thestandard deviation. - Dothis for all the Xs and for Y. |
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What is the value of the standardizedintercept (always)? |
0 |
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What information does a standardizedcoefficient give? |
GivesSD change in Y for a 1 SD change in X |
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What is partial r squared a proportion of? |
Proportionsof variance accounted for by a predictor that is not accounted for by otherpredictors |
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What is semipartial r squared a proportion of? |
denominatoris all variance in Y/num is all variance accounted for by a predictor |
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Which will be bigger for a predictor—partial rsquared or semipartial r squared? |
- Thedenominator of sr2 is almost always larger than the denominator ofpr. -Thismeans pr2 ≥ sr2, and in most circumstances, pr2> sr2. |
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How is semipartial r squared calculated? |
Iscalculated as the increase in overall R2 that comes from adding thepredictor to the model. |
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In which direction is R2 biased(too big or too small)? |
Ittends to overestimate (too big) its true value p2 |
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What is the relationship between R2and shrunken R2? (Which will be larger?) |
- Shrunken( or adjusted) R2 reduces the overestimation bias of R2 - ShrunkenR2 reduces R2 based on how many predictors (k) are in themodel versus how big the sample is (n) - When k is very small compared to n, shrunken R2is nearly equal to R2 - When k is large relative to n, shrunken R2shrinks a lot. |
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What is the difference between hierarchicaland non-hierarchical regression in the order in which predictors are entered? |
- Hierachicalregression: Predictors are entered in order/in steps. -Non-hierarchicalregression: Predictors are entered at the same time. |
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When two (or more) predictors overlap invariance they account for in Y, to which predictor is the overlapping varianceaccounted for attributed to? |
The one which was entered first |
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What are the general rules for orderingpredictors in hierarchical regression? |
- Ifpredictors are known to cause each other, put the causes before the effects. - Theoreticalreasons to enter things first |
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When predictors are entered one at a time, whatis the relationship between the values of the F test of R2 changeand the t-test for each coefficient? |
o F =T2 for coefficient |
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When predictors are entered one at a time, What is the relationship between their p-values? |
o pvalues will be significant |
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How can R2 change when a predictoror set of predictors is added to the model? Can it increase? Stay the same?Decrease? |
It can increase or stay the same, but never decrease |
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How does the numerator df for the F test of R2change related to the number of predictors added? |
usesk, so adding predictors in numerator and take it from degrees of freedom in thedenominator in the previous step |
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How does the R2 for the final stepof a hierarchical regression compare to the R2 for anon-hierarchical regression with the same predictors? |
Itwill be the same as a multiple regression run from the same set of predictors |
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Which will typically yield more significancefor predictors, a hierarchical or a non-hierarchical regression? |
o Hierarchicalregression will generally yield more sig coefficients than non-hierarchicalregression (slide 40) o Becausevariance is attributed to some predictor |
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When predictors are entered as sets, and twoor more predictors in the same setaccount for overlapping variance in Y, to which predictor is the overlappingvariance accounted for attributed to? |
- Attributedto neither - Likerunning multiple regression within that set |
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What is the order of X2? of X? |
- Orderhere refers to the sum of the powers the predictor is raised by for each term,: -X2 is of order 2 -X is of order 1( x=x1) -The intercept is of order 0 ( it is multipliedby 1(=x0)) |
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In the regression Y(hat) = B0 + B1X+ B2X2, which coefficient is unconditional? Whichcoefficients are conditional? |
Unconditional - B2 Conditional – B0 and B1 |
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What information does B2 give in the regression Y(hat) = B0 + B1X + B2X2? What information does B1 give? What informationdoes B0 give? |
- B2 givesinformation about the entire curve - B1 gives slopeof line tangent to curve at X=0 - B0 gives Yintercept at x=0 |
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Which of B2, B1, and B0will change when we center X? Why will they change? |
B1 AND B0 because they are conditional |
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What sign of B2 is associated withan upward bending curve? With a downward bending curve? |
Positive=upward bending curve Negative=downward bending curve |
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What is a simple slope? |
Simple slope is the slope of tangent line to the curve at X=0 |
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What does centering at the mean of X do to thecorrelation between X and X2? Does it increase it, reduce it, orkeep it the same? |
Centering at X(bar) reduces rxx2 by a lot (slide 34 and 35) makes it smaller in magnitude reduces non-essential multicollinearity Reducesthe standard error for the test of b1 |
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What does centering at the mean of X do to thestandard error of B1? Does it increase it, reduce it, or keep it thesame? |
Reduces it |
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What value do we center at if we want B1to represent the average slope of tangent lines to the curve across the rangeof the data? |
Center at the mean Average of the slopes at all those tangent lines on the curves |
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In the regression Y(hat) = B0 + B1X+ B2X2 + B3X3, which coefficient isunconditional? Which coefficients are conditional? |
- B3 is unconditional - B0,b1, b2 are conditional |
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What information does B3 give in the regression Y(hat) = B0 + B1X + B2X2 + B3X3? What information does B2 give? What informationdoes B1 give? What information does B0 give? |
- It tells the shape of the entire curve - B2 gives the bend of the tangent curve at x=0 - B1 gives the slope of the line tangent to the curve at x=0 - b0 gives the height of the curve at x=0 |
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If we enter X3 in a regressionmodel, which other terms must also be included? If we enter X2,which other term must also be included? |
- Other terms – all lower order terms x2, x, and b0 - We must include coefficient for x and the intercept |
