5Beispiel: MLU & Age Child Age in months MLU 1 2 3 4 5 6 7 8 9 10 11 12 24233220435828345346493220.127.116.11.932.645.631.918.104.22.1683.212.84
6Beispiel: MLU & AgeLong: There is an association between age and MLU. The r of .887 showed that 78.6% (r2) of the variation in MLU was accounted for by the variation in age. The associated probability level of showed that such a result is unlikely to have arisen from sampling error.Short: As can be seen in the table above, there is a strong correlation between age and MLU (r = .887, p = .001).
8Beispiel: Typicality & Frequency Kendall’s tau ( = .733, p = .003) Spearman’s rho (rs = .879, p = .001)
9Partial correlationPhoneme & Silben r = .898, p = .001 Phoneme & Häufigkeit r = .795, p = .006 Silben & Häufigkeit r = .677, p = .031Phoneme & Häufigkeit r = .578, p = .103 (Silben Konstant)
10Nominal DatenEs gibt eine signifikante Korrelation zwischen Geschlecht (Boys vs. Girls) und der Präferenz für ein bestimmtes Spielzeug (mechanisch vs. nicht-mechanisch) (χ2 = 49,09, df = 2, p = .001).Phi-Koeffizient = .70, p < .001 Cramer’s V = .70, p < .001
12Correlation - Regression Correlational analysis gives us a measure that represents how closely the data points are associated.Regression analysis measures the effect of the predictor variable x on the criterion y. – How much does y change if you change x.A correlational analysis is purely descriptive, whereas a regression analysis allows us to make predictions.
13Types of regression analysis Predictor variableCriterion (target) variableLinear regression1 interval
14Types of regression analysis Predictor variableCriterion (target) variableLinear regression1 intervalMultiple regression2+ (some of the variables can be categorical)
15Types of regression analysis Predictor variableCriterion (target) variableLinear regression1 intervalMultiple regression2+ (some of the variables can be categorical)Logistic regressionDiscriminant analysis1+1 categorical
17Linear Regression y = bx + a y = variable to be predicted x = given value on the variable x b = value of the slope of the line a = the intercept (or constant), which is the place where the line-of-best-fit intercepts the y-axis.
18Linear RegressionGiven a score of 20 on the x-axis, a slope of b = 2, and an interception point of a = 5, what is the predicted score?y = (2 20) + 5 = 45
19Beispiel: MLU & Age How much does MLU increase with growing age? Child Age in monthsMLU1234567891011122423322043582834534649322.214.171.124.932.645.631.9126.96.36.1993.212.84How much does MLU increase with growing age?
20Linear RegressionThere is s strong association between age and MLU (R = 0.887). Specifically, it was found that the children’s MLU increases by an average of .088 words each months (t = 6,069, p < 0.001), which amounts to about a word a year. Since the F-value (36,838, df = 1) is highly significant (p < 001), these results are unlikely to have arisen from sample error.
21Several predictor variables influence the criterion. Multiple RegressionSeveral predictor variables influence the criterion.Plane-pf-best-fit1. Simultaneous multiple regression 2. Stepwise multiple regression
22Simultaneous Multiple Regression Eine Universität möchte wissen, welche Faktoren am besten dazu geeignet sind, den Lernerfolg ihrer Studenten vorherzusagen. Als Indikator für den Wissensstand der Studenten gilt die Punktzahl in einer zentralen Abschlussklausur. Als mögliche Faktoren werden in Betracht gezogen: (1) Punktzahl beim Eingangstest, (2) Alter, (3) IQ Test, (4) Punktzahl bei einem wissenschaftlichen Projekt.
23Predictor entrance exam age IQ Scientific project Simultaneous Multiple RegressionPredictor entrance exam age IQ Scientific projectCriterion final exam
24There is s strong association between the predictor variables and the result of the final exam (Multiple R = 0.875; F = 22,783, df = 4, p = .001 ). Together they account for 73% of the variation in the exam succes. If we look at the four predictor variables individually we find that the result of the entrance exam (B = .576, t = 5.431, p = .001) and the IQ score (B = .447, t = 4.606, p = .001) make the strongest contributions (i.e. they are the best predictors). The predictive value of age (B = .099, t = 5.431, p = .327 and the score on the scientific project is not significant (B = 0.141, t = 1,417, p = ).
25Stepwise Multiple Regression In stepwise regression you begin with one independent variable and add one by one. The order of addition is automatically determined by the effect of the independent variable on the dependent variable.
26Assumptions Multiple Regression 1. At least 15 cases2. Interval data3. Linear relationship between predictor variables and criterion.4. No outliers (or delete them)5. Predictor variables should be independent of each other
27Logistic RegressionIn Linguistics, you often use logistic regression: Multiple factors determine the choice of linguistic alternates: 1. look up the number - look the number up 2. that-complement clauses - zero-complement clause 3. intial adverbial clause - final adverbial clause 4. aspirate /t/ - unaspirated /t/ - glottal stop - flap