Kwantitatieve methoden
Week 1
Regression analysis
Quantitative technique to understand relationships among variables
Vocabulary
1. Dependent variable (Y) = to be explained
2. Independent variable (X) = explained
3. Regress Y on X
Correlation coefficient
Degree/strength of association between 2 (!) variables
= standardized covariation between two variables X and Y
Vocabulary
1. Covariance (X, Y) = sum of product of deviances in X and Y for all data points i
2. Variance = sum of squared deviances in X
3. Deviance = difference own value and standardized value
(mean – own)
Significance testing
1. Ensure assumptions are met
a. Random samples -> same chance for everyone to be choosen
b. Independent samples
c. Interval-ratio level of measurement
d. Sampling distribution is normally distributed
2. Formulate hypotheses
a. Geen richting
i. H0: = 0
ii. H1: 0
b. Negatief effect
i. H0: ≥ 0
ii. H1: < 0
c. Positief effect
i. H0: ≤ 0
ii. H1: > 0
3. Determine critical area from the appropriate sampling distribution
a. Reject H0 if
i. Calculated Z is smaller than needed Z -> test statistic < critical value
ii. P is smaller than 0,05
4. Calculate the test statistic
5. Make decision
6. State conclusions
1
, Week 2
Bivariate regression: Ordinary Least Squares Estimation
Regression equation
1. Y= a + bX + e
2. Y = true value
3. A = intercept = value of Y for X = 0
4. B = slope = change in Y as a consequence of change in X
5. E = residual = actual value – predicted value = Y −Y^
Total deviation = explained deviation + unexplained deviation (residual)
Best fit line -> minimizes squared distances between point and line
R2 = the proportion of variation explained by the regression = the % variation explained =
squared correlation coefficient = how well can the DV be predicted from knowledge of IVs
Book
Relatie regressie en correlatie -> beide gaan ervan uit dat de relatie tussen afhankelijke en
onafhankelijke variabelen bepaald kan worden door een rechte lijn
1. Regressie: focus op slope van de lijn
2. Correlatie: degree van punten langs de lijn
Week 3
Regression vs Correlation
Similarities
1. Both assume a linear relationship
2. Test of significance of correlation coefficient = test of significance of bivariate
regression slope
Differences
1. Regression: slope + intercept of line -> magnitude of relationship
2. Correlation: degree to which points are scattered along the line -> strength of
association
Bivariate Regression Analysis (No computer)
1. Compute slope
2. Compute intercept
3. Compute R2
4. Test of significance and conclusions (week 1)
Bivariate Regression Analysis (With computer)
1. State hypothesis in words + symbols
2. Ensure assumptions are met
3. Estimate regression with SPSS
4. Display results in results table
5. State results of significance tests (p-value)
6. Interpret relevant statistics
7. Prediction and conclusion
2
Week 1
Regression analysis
Quantitative technique to understand relationships among variables
Vocabulary
1. Dependent variable (Y) = to be explained
2. Independent variable (X) = explained
3. Regress Y on X
Correlation coefficient
Degree/strength of association between 2 (!) variables
= standardized covariation between two variables X and Y
Vocabulary
1. Covariance (X, Y) = sum of product of deviances in X and Y for all data points i
2. Variance = sum of squared deviances in X
3. Deviance = difference own value and standardized value
(mean – own)
Significance testing
1. Ensure assumptions are met
a. Random samples -> same chance for everyone to be choosen
b. Independent samples
c. Interval-ratio level of measurement
d. Sampling distribution is normally distributed
2. Formulate hypotheses
a. Geen richting
i. H0: = 0
ii. H1: 0
b. Negatief effect
i. H0: ≥ 0
ii. H1: < 0
c. Positief effect
i. H0: ≤ 0
ii. H1: > 0
3. Determine critical area from the appropriate sampling distribution
a. Reject H0 if
i. Calculated Z is smaller than needed Z -> test statistic < critical value
ii. P is smaller than 0,05
4. Calculate the test statistic
5. Make decision
6. State conclusions
1
, Week 2
Bivariate regression: Ordinary Least Squares Estimation
Regression equation
1. Y= a + bX + e
2. Y = true value
3. A = intercept = value of Y for X = 0
4. B = slope = change in Y as a consequence of change in X
5. E = residual = actual value – predicted value = Y −Y^
Total deviation = explained deviation + unexplained deviation (residual)
Best fit line -> minimizes squared distances between point and line
R2 = the proportion of variation explained by the regression = the % variation explained =
squared correlation coefficient = how well can the DV be predicted from knowledge of IVs
Book
Relatie regressie en correlatie -> beide gaan ervan uit dat de relatie tussen afhankelijke en
onafhankelijke variabelen bepaald kan worden door een rechte lijn
1. Regressie: focus op slope van de lijn
2. Correlatie: degree van punten langs de lijn
Week 3
Regression vs Correlation
Similarities
1. Both assume a linear relationship
2. Test of significance of correlation coefficient = test of significance of bivariate
regression slope
Differences
1. Regression: slope + intercept of line -> magnitude of relationship
2. Correlation: degree to which points are scattered along the line -> strength of
association
Bivariate Regression Analysis (No computer)
1. Compute slope
2. Compute intercept
3. Compute R2
4. Test of significance and conclusions (week 1)
Bivariate Regression Analysis (With computer)
1. State hypothesis in words + symbols
2. Ensure assumptions are met
3. Estimate regression with SPSS
4. Display results in results table
5. State results of significance tests (p-value)
6. Interpret relevant statistics
7. Prediction and conclusion
2
