Lecture 20: Correlation & Simple Regression

Question 1

What is the Pearson product-moment correlation coefficient (PPMCC) and from which values does it range

Answer 1

It is a measure of the linear correlation between variables X and Y
It is standardized and thus ranges between -1 and +1, where -1 means a total negative correlation, 0 means no correlation and +1 means a total positive correlation

Question 2

What are the 3 most important assumptions for linear regression with 1 predictor variable and what do they entail

Answer 2

1. Sensitivity; there is a certain sensitivity of the results to outliers - influence of outliers
2. Homoscedasticity; variance of residuals should be equal across all expected values (look at scatterplot of standardized: predicted values x residuals)
3. Linearity; continuous dependent and predictor variables are linearly related

Question 3

What are the 6 ways of assessing an association

Answer 3

1. Correlation between X and Y, standardized between -1,1
2. Covariance between X and Y, unstandardized
3. Regression coefficient in linear regression, standardized
4. T-statistic: standardized difference between b1 and b0
5. The correlation between Y and model prediction, standardized (between -1,1)
6. F: signal to noise ratio of a model
   —> the last two metrics are more indicative of an overall model’s performance

Question 4

What does the b1 and b0 stand for in the regression formula

Answer 4

B1 = the slope
B0 = the intercept

Question 5

What is the least squares estimate

Answer 5

The regression line that is closest to all the data points, which means that the squares are as low as possible