Bivariate regression Flashcards
What is the purpose of a bivariate regression?
To find a numerical representation of the fixed relationship between an observed response variable and a number of explanatory variables
What are residuals?
The disturbances, unsystematic variations response
Also measurement error
What is the OLS?
Ordinary Least Squares estimation
- fits linear trend through ‘cloud’ of data points
- minimiss te squared residuals from the regression line
What data shows how important graphs are?
Anscombe’s data (1973)
- Showed the same regression line can be drawn through a variety of different points
What are the 3 approaches to regression analysis?
Confirmatory
Exploratory
Catch-all plots
What is the confirmatory approach?
Significance tests, inferring from sample to population (guarding against sampling error)
Presumes well developed model
Necessitates demanding assumptions
What is exploratory approach?
Graphs of residuals
Exemplifies problems with data and models
Tries to develop initial models into an improved/better model
What are Catch-all plots?
Can be used in multiple regression
Magnifies any defects
General diagnostic tool
Detect different model ills
What are the model assumptions?
Zero mean for the residuals
No autocorrelation between error terms
Homoscedacity (equal variance in error)
Zero correlation between errors and predictor variables
Havent fitted linear function to non linear data
What did Hookers data show?
Art of exploration
Pressure as some function of Boiling point of water
Have to remove outliers and refit the model
What is the general scheme for model reformulation?
Transformation
Omission of data observations
Additional Variables
(BUT need to justify decisions)
