Everything Flashcards
What is the simple linear regression formula?
Y i=b0+b1Xi+ui
What is Yi?
The dependent variable (e.g persons income)
What is Xi?
The independent variable (e.g persons education)
What is b0?
the intercept
Y when X=0
what is B1
the slope
how much Y changes for a one unit increase in X
what is Ui?
the error term
What is the OLS?
Ordinary Least Squares
It is the method to find the line of best fit
What is a residual?
u with an arrow on top
it is the difference between the observed value and the predicted value of the dependent variable in the sample regression
What is TSS?
It is the total square Sum
What is ESS?
It is estimated sum of squares
What is RSS?
it is Residual sum of squares
How do we find a residual?
Residual = Yi - Y^i
What is the OLS formula for the slope (b1)
look at notes
How can you interpret b1 (slope)?
it shows the relationship strength,
positive slope = positive correlation
negative slope = negative correlation
how can you interpret a (intercept)?
GIves baseline for when x = 0
what is the formula for goodness of fit (R^2)
1- Sum of squared residuals (SSR) / Total Sum of Squares (TSS)
what is the formula for the intercept (b0)
b0 = Y(mean with dash on top) - b1X (mean with dash on top)
What are the OLS assumptions?
Linearity:
No Perfect Multicollinearity
Homoscedasticity:
No Autocorrelation:
Zero Conditional Mean
What is Linearity?
Relationship between X and Y is linear
What is No perfect multicollinearity?
Independent variables are not perfectly correlated to eachother
What is Homoscedasticity?
Variance of error terms (ui) is constant for all values of X
What is No Autocorrelation
Error terms are uncorrelated across observations
What is Zero Conditional Mean?
E(u∣X)=0, meaning the error term has no systematic pattern
What is the null hypothesis?
represents no effect or no difference
H0: B1 = 0
What is the alternative hypothesis?
H1: B1 not equal to 0
opposes Null hypothesis
what is the significance level?
a
How do you calculate RSS?
- calulate the residual
- Square each one and the add them
What is F test used for?
It is used to test the joint significance of multiple coefficients
Where can u find the F test formula?
formula sheet
what is perfect collinarity?
when the independent variables have linear relationships
When should you use the chow test?
when there is a structural break in the data
What is Heteroscedasticity?
When the variance of error terms in a regression is not constant
What are the consequences on OLS?
It makes them still unbiased but inaccurate as the standard errors are no longer valid
also makes statistical tests unreliable
How can you detect Heteroscedasticity?
BY either graphing or doing a white test
