## Tuesday, May 4, 2010

### Inference, Hypothesis Testing, & Regression

Inference: the exercise of providing information about the population based on information contained in the sample

Type 1 Error: rejecting a true null hypothesis
- the probabability of rejecting a true null hypothesis ( or the probability of a type 1 error) is equal to alpha or 'α' This is also the same as the level of significance in a hypothesis test.

Type II Error: failing to reject, or loosely speaking, 'accepting' the null hypthesis when it is false
-the probability of a type II error =beta or β

Power: the probability of rejecting the null hypothesis when it is false. (1-β)

Regression Model: describes how the dependent variable (y) is related to the independent variable (x), also known as the least squares line.

y = b0 + b1*x

This is derived by the process of least squares, which gives the value for the slope (b1) and the intercept (bo) that minimizes the sum of the squared deviations between the observed values of the dependent variable (Y) and the estimated values of the dependent variable (Y*).

Co-efficient of determination(R-squared) = SSR/SST -> gives the proportion of total variation explained by the regression model. Larger values indicate that the sample data are closer to the least squares line, or a stronger linear relationship exists.