Fichas
OLS, R squared and correlation coefficient
Fichas del conjunto (17)
- 1What is the least squares principle?The OLS minimises the sum of the squared deviations of the vertical distance from the estimated error terms to the estimated regression line
[Also known as residual sum of squares] - 2Why do we care about this?We run into a problem in stats when we're trying to fit a line to data points in a scatter plot. The problem is this: It's hard to say for sure which line fits the data best. (khan academy)
We want to draw the best estimated regression line for a data set, and minimising RSS is a good way of doing this. - 3How does OLS work?It wants to minimise RSS, and the best way it can do this is by calculating the coefficients of the IVs (remember that the error term captures the non-deterministic components of the regression)
- 4What is the OLS formula for calculating the RSS minimising coefficients?
- 5What is the TSS?It is the decomposition of variance
TSS=Explained sum of squares + Residual sum of squares - 6TSS formula? (write down)check slides
- 7How to determine if it is a 'best fit' line?Use Rsquared.
[R^2 is the ratio of explained sum of squares to the total sum of squares]
Since OLS minimises RSS, and TSS=ESS+RSS, then OLS should provide the largest R^2 possible - 8What is the R^2 formula (Write it down)check slides
- 9How to interpret R^2?Since its a ratio, 0
- 10What is the problem with using R^2?1. The R^2 value increases with every additional IV
If we interpreted this, every added variable helps the line become a better fit
Problem: Adding nonsense variables also improves the fit of the line! - 11What is the problem with using R^2?2. To get a good R^2, you need more variables, which reduces the equation's degrees of freedom
Problem: The lower the degrees of freedom, the less reliable the estimates - 12What is the adjusted R^2?The adjusted R2 measures the percentage of the variation of Y around its mean that is explained by the regression equation, adjusted for the degrees of freedom.
Range: (slightly below 0)< Adj R^2<1 - 13Adjusted R^2 formula? (Write down)Check slides
- 14Why is adjusted R^2 better?1. It can increase, decrease or remain constant unlike R^2.
For adjusted R^2 to increase, the addition of the new variable must outweigh the loss of the degree of freedom (the addition must enhance the model more than what can be predicted by chance) - 15Why is adjusted R^2 better?2. Can be used to compare the fits of regressions with the same DV but different number of IVs
- 16Can adjusted R^2 be misused?Yes, if an added coefficient has an implausible sign, it might not be a useful regression e.g. saying water consumption (DV) rises when the price of water (additional IV) increases
In this case, use common sense: The higher adjusted R^2 is not worth it if the line does cannot be interpreted sensibly - 17What is the simple correlation coefficient, r?r measures the strength and direction of the linear relationship between two variables:
r=+1:the two variables are perfectly positively correlated
r=–1:the two variables are perfectly negatively correlated
r = 0:the two variables are totally uncorrelated
Información
- Descripción
- Fichas sobre OLS, R squared and correlation coefficient, creado por Felix Culas el 05/04/2017.
- Creado por
- Felix Culas · abr 2017
- Actualizado
- 5 abr 2017
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- 2
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