Algemeen
𝑝 − 𝑤𝑎𝑎𝑟𝑑𝑒 < 0,05 → 𝐻! 𝑣𝑒𝑟𝑤𝑒𝑟𝑝𝑒𝑛
𝑝 − 𝑤𝑎𝑎𝑟𝑑𝑒 > 0,05 → 𝐻! 𝑎𝑎𝑛𝑣𝑎𝑎𝑟𝑑𝑒𝑛
Slide Naam formule Formule Wat Opmerkingen
Total variation in the response = variation explained by the
1A.13 SSTO = SSR + SSE model + unexplained variation
Test the statistical significance of the model: is the model
1A.17 F-test significantly better than the empty model
1A.19 t-test Test the significance of the contribution of 𝑥"
Geeft aan welk percentage van de variantie in Y verklaard
1A.21 R2 SSR / SSTO wordt door het regressiemodel
(𝑛 − 1)(1− 𝑅# )
1−
1A.21 R2adj 𝑛 −𝑘 − 1 Penaliseert voor het toevoegen van irrelevante X'en
𝜎: ≈ 𝑀𝑆𝐸
𝜇 𝑦@
1A.21 Coefficient of variation Meet de relatieve spreiding ten opzichte van het gemiddelde
Check the increase in SSR by sequentially adding variables
1A.25 type-I SS to the model
Gives the decrease in SSE by adding a variable to the model
which contains all the other variables except the interaction
1A.27 type-II SS terms including that variable
Gives the increase in SSR (or decrease in SSE) by adding a for models without interaction; type-II SS =
1A.28 type-III SS variable to the model which contains all the other variables type III
1
𝑉𝐼𝐹$ =
1A.32 Variance Inflation Factor (VIF) 1 − 𝑅#$ Check for multicollinearity if VIF > 10: serious multicollinearity
1A.31 Compare type I & II SS Check for multicollinearity if significant difference -> multicollinearity
2(𝑘 + 1) difference between good and bad leverage
1A.37 ℎ$$ > i-th observation has an extreme x-value points
𝑛
1A.40 for 30 < n < 100 𝑖𝑓 𝑑𝑓𝑓𝑖𝑡𝑠 > 1 i-th observation is influential
2∗ 𝑘+1
1A.40 for large n 𝑛 i-th observation is influential
1A.41 Cook's distance 𝐷 $ > 𝐹%&',)*%*'(0,50) i-th observation is influential
Tests wether the same model is valid in 2 groups or in 2
Chow test
1A.58 periods
1B13 MSR Measures the differences between the group means
1B13 MSE Measures the variation within the groups
1B13 ANOVA Test for siginficant differences between the means
𝑀𝑆𝑅 Probability that nulhypothesis is rejected
𝑃( > 𝐹+*',)*+ 1 − 𝛼) 𝐻, 𝑡𝑟𝑢𝑒 )
1B16 Power 𝑀𝑆𝐸 while Ha is true
1B24 Tukey test all the pairwise comparisons, gives confidence intervals
1B28 Bonferroni method is used to derive simultaneous confidence intervals
Goal is to improve the power (reduce the unexplained
1B45 ANCOVA variance)
Check wether the effect of the covariate is the same for each
1B52 ANCOVA factor level
1B54 ANCOVA if no interaction; test the treatment main effect
if no interaction; test wether there is a significant covariate
1B55 ANCOVA effect
1B61 Two way anova Test interaction effect Compare SS <-> full model
1B65 Two way anova if no interaction; test main effects of both factors
1B67 Factor level effects Zoeken waar het verschil zit bij two way anova
1B77 Random block effects Blocks are now a random sample of all possible blocks
1B82 Repeated measures A random block = random test person
2.21 Durbin Watson test 𝑑𝑤 = 2 − 2𝜌R = 2 − 2corr(𝑢- , 𝑢-*' ) in heteroscedasticity case
2.23 Cochrane-Orcutt in heteroscedasticity case & AR(1) residuals
2.28 Newey and West Assume residuals are autocorrelated and heteroscedastic
2.30 Breusch-Godfrey Check autocorrelation in autoregressive models also called Lagrange multiplier
2.40 Instrumental Variables Estimation 𝑖𝑓 𝑐𝑜𝑟𝑟 𝑥. , 𝑢 ≠ 𝑂; 𝑜𝑛𝑒 𝑐𝑎𝑛 𝑔𝑒𝑡 𝑐𝑜𝑛𝑠𝑖𝑠𝑡𝑒𝑛𝑡 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑜𝑟𝑠 𝑢𝑠𝑖𝑛𝑔 𝐼𝑉 is a 2 step procedure
2.48 Wu-hausman test test for endogeneity if reject H0; use IV (don't want that)
𝑡𝑒𝑠𝑡𝑖𝑛𝑔 𝑤𝑒𝑡ℎ𝑒𝑟 𝜙 = 1 𝑖𝑠 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑡𝑜 Φ = 0 Add lags with Breusch-Godfrey to get rid of
2.57 unit-root nonstationarity autocorrelated residuals
Get correct p-values after adding lags with the Breusch
Godfrey test + applying OLS to the fitted model with lags (if
2.63 Augmented Dickey Fuller test needed)
We test the residuals of the OLS regression for a unit root, if
2.70 Engle-Granger test there is none -> series are cointegrated
𝑡𝑒𝑠𝑡 𝐻! : 𝑐𝑜𝑟𝑟 𝜈 $, 𝑥$- = 0 if accept: use random effects estimator
2.91 Hausman test if reject: use fixed effects estimator
𝜋$
3A.5 odds 1 − 𝜋$ Altijd tussen 0 en 1
3A.5 logit ln(odds)
3A.11 Likelihood ratio test test the significance of the model
3A.11 Score test / Lagrange multiplier test test the significance of the model
3A.12 Wald test test the significance of the model with Mahalanobisdistance
Can only be used to compare different models
test the significance of the model, with a correction for the fitted on the same data (smaller criterion =
3A.14 AIC and BIC degrees of freedom better)
3A.15 Standardnormal test Significance of individual parameters Bij grote steekproeven
3A.15 Wald test Significance of individual parameters Squared version of standardnormal test
3A.22 (dis)Concordant pairs Check how well model classifies
3A.36 Cumulative logit model for ordered response values
no ordered response value and classification depends on
characteristics of the item to be classified or the person that only the difference between parameters is
3A.36 Multinomial logit model has to make the choice estimable
𝑝 − 𝑤𝑎𝑎𝑟𝑑𝑒 < 0,05 → 𝐻! 𝑣𝑒𝑟𝑤𝑒𝑟𝑝𝑒𝑛
𝑝 − 𝑤𝑎𝑎𝑟𝑑𝑒 > 0,05 → 𝐻! 𝑎𝑎𝑛𝑣𝑎𝑎𝑟𝑑𝑒𝑛
Slide Naam formule Formule Wat Opmerkingen
Total variation in the response = variation explained by the
1A.13 SSTO = SSR + SSE model + unexplained variation
Test the statistical significance of the model: is the model
1A.17 F-test significantly better than the empty model
1A.19 t-test Test the significance of the contribution of 𝑥"
Geeft aan welk percentage van de variantie in Y verklaard
1A.21 R2 SSR / SSTO wordt door het regressiemodel
(𝑛 − 1)(1− 𝑅# )
1−
1A.21 R2adj 𝑛 −𝑘 − 1 Penaliseert voor het toevoegen van irrelevante X'en
𝜎: ≈ 𝑀𝑆𝐸
𝜇 𝑦@
1A.21 Coefficient of variation Meet de relatieve spreiding ten opzichte van het gemiddelde
Check the increase in SSR by sequentially adding variables
1A.25 type-I SS to the model
Gives the decrease in SSE by adding a variable to the model
which contains all the other variables except the interaction
1A.27 type-II SS terms including that variable
Gives the increase in SSR (or decrease in SSE) by adding a for models without interaction; type-II SS =
1A.28 type-III SS variable to the model which contains all the other variables type III
1
𝑉𝐼𝐹$ =
1A.32 Variance Inflation Factor (VIF) 1 − 𝑅#$ Check for multicollinearity if VIF > 10: serious multicollinearity
1A.31 Compare type I & II SS Check for multicollinearity if significant difference -> multicollinearity
2(𝑘 + 1) difference between good and bad leverage
1A.37 ℎ$$ > i-th observation has an extreme x-value points
𝑛
1A.40 for 30 < n < 100 𝑖𝑓 𝑑𝑓𝑓𝑖𝑡𝑠 > 1 i-th observation is influential
2∗ 𝑘+1
1A.40 for large n 𝑛 i-th observation is influential
1A.41 Cook's distance 𝐷 $ > 𝐹%&',)*%*'(0,50) i-th observation is influential
Tests wether the same model is valid in 2 groups or in 2
Chow test
1A.58 periods
1B13 MSR Measures the differences between the group means
1B13 MSE Measures the variation within the groups
1B13 ANOVA Test for siginficant differences between the means
𝑀𝑆𝑅 Probability that nulhypothesis is rejected
𝑃( > 𝐹+*',)*+ 1 − 𝛼) 𝐻, 𝑡𝑟𝑢𝑒 )
1B16 Power 𝑀𝑆𝐸 while Ha is true
1B24 Tukey test all the pairwise comparisons, gives confidence intervals
1B28 Bonferroni method is used to derive simultaneous confidence intervals
Goal is to improve the power (reduce the unexplained
1B45 ANCOVA variance)
Check wether the effect of the covariate is the same for each
1B52 ANCOVA factor level
1B54 ANCOVA if no interaction; test the treatment main effect
if no interaction; test wether there is a significant covariate
1B55 ANCOVA effect
1B61 Two way anova Test interaction effect Compare SS <-> full model
1B65 Two way anova if no interaction; test main effects of both factors
1B67 Factor level effects Zoeken waar het verschil zit bij two way anova
1B77 Random block effects Blocks are now a random sample of all possible blocks
1B82 Repeated measures A random block = random test person
2.21 Durbin Watson test 𝑑𝑤 = 2 − 2𝜌R = 2 − 2corr(𝑢- , 𝑢-*' ) in heteroscedasticity case
2.23 Cochrane-Orcutt in heteroscedasticity case & AR(1) residuals
2.28 Newey and West Assume residuals are autocorrelated and heteroscedastic
2.30 Breusch-Godfrey Check autocorrelation in autoregressive models also called Lagrange multiplier
2.40 Instrumental Variables Estimation 𝑖𝑓 𝑐𝑜𝑟𝑟 𝑥. , 𝑢 ≠ 𝑂; 𝑜𝑛𝑒 𝑐𝑎𝑛 𝑔𝑒𝑡 𝑐𝑜𝑛𝑠𝑖𝑠𝑡𝑒𝑛𝑡 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑜𝑟𝑠 𝑢𝑠𝑖𝑛𝑔 𝐼𝑉 is a 2 step procedure
2.48 Wu-hausman test test for endogeneity if reject H0; use IV (don't want that)
𝑡𝑒𝑠𝑡𝑖𝑛𝑔 𝑤𝑒𝑡ℎ𝑒𝑟 𝜙 = 1 𝑖𝑠 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑡𝑜 Φ = 0 Add lags with Breusch-Godfrey to get rid of
2.57 unit-root nonstationarity autocorrelated residuals
Get correct p-values after adding lags with the Breusch
Godfrey test + applying OLS to the fitted model with lags (if
2.63 Augmented Dickey Fuller test needed)
We test the residuals of the OLS regression for a unit root, if
2.70 Engle-Granger test there is none -> series are cointegrated
𝑡𝑒𝑠𝑡 𝐻! : 𝑐𝑜𝑟𝑟 𝜈 $, 𝑥$- = 0 if accept: use random effects estimator
2.91 Hausman test if reject: use fixed effects estimator
𝜋$
3A.5 odds 1 − 𝜋$ Altijd tussen 0 en 1
3A.5 logit ln(odds)
3A.11 Likelihood ratio test test the significance of the model
3A.11 Score test / Lagrange multiplier test test the significance of the model
3A.12 Wald test test the significance of the model with Mahalanobisdistance
Can only be used to compare different models
test the significance of the model, with a correction for the fitted on the same data (smaller criterion =
3A.14 AIC and BIC degrees of freedom better)
3A.15 Standardnormal test Significance of individual parameters Bij grote steekproeven
3A.15 Wald test Significance of individual parameters Squared version of standardnormal test
3A.22 (dis)Concordant pairs Check how well model classifies
3A.36 Cumulative logit model for ordered response values
no ordered response value and classification depends on
characteristics of the item to be classified or the person that only the difference between parameters is
3A.36 Multinomial logit model has to make the choice estimable
