Bivariate statistical measures of regression and correlation

1. Problems with regression

1.1. non-homogeneous variance

1.2. non-linear relationship

1.3. correlated errors

2. Regression analysis

2.1. studies the relationship between two variables

2.2. statistical technique used to derive an equation that relates a criterion variable to one or more predictor variables.

2.3. studies the strength of association through a measure of association called relationship coefficient

3. Variant statistical measures

3.1. relacion y correlacion

3.2. scatter diagram

3.3. simple linear regression

3.4. multiple linear regression

3.5. correlation

4. Regression analysis model

4.1. Statistical: allows the incorporation of a random component in the relationship

4.2. Standardized: the slope tells us if there is a relationship between two variables

4.3. Deterministic: that under ideal conditions the variable independently can be due to a mathematical function of the independent variables

5. Linear regression

5.1. Pearson linear correlation coefficient

5.1.1. without the points it has a tendency to be arranged in alignment

5.1.2. It is useful to determine if there is a relationship between two variables, but it will not work for quadratic, logarathmic

5.2. Covariance of two random variables X,Y

5.2.1. between two variables x, y tells us if the relationship between two variables is direct or inverse

5.2.2. The sign of the covariance tells us that the ni¿ of the points is increasing or not, but it does not say anything about the degree of the relationship of variables

6. Simple linear regression model

6.1. we find a very simple linear function of -y=bo+bx