Multiple regression analysis Flashcards
Why do you need a multiple regression
To prevent an explanatory variable ending up in the u term. Therefore prevents ZCM assumption being broken
MLR. 3
No prefect collinearity - No exact linear relationships. Also no constant explanatory variables
MLR. 6
No correlation between error terms - no autocorrelation
Significance level
Measure of the strength of evidence that must be present
Critical value
A point which is compared to the test statistic. If t value is greater than CV then Ho can be rejected
Type 1 error
When the actual state is false but the analysis says it’s true
Type 2 error
When the actual state is true but the analysis says it’s false
P value with example
Summary of strength of evidence against the null.
E.g - p = 0.05 then you can be 95% sure it is statistically significant
F test
Used to compare multiple regressions against each other. e.g an unrestricted model and restricted model
Reading f statistic (the degrees of freedom)
Numerator degrees of freedom on top (same value as q). Denominator degrees of freedom on the left hand side
Why are quadratics needed in regression?
For increasing or decreasing marginal effects. E.g - experience on wage diminishes
Why are logs needed in regression?
Useful for large amounts.
Also often reduces heteroskedasticity.
Finding a maximum point from a quadratic
When B1 intercept is positive and B2 is negative. x* is when B1/2B2
Level - Level
B hat (mean of X/ mean of Y)
Level - Log
B hat (1 / mean of Y)
Log - Level
B hat * mean of X
Log - Log
B hat
What is the t statistic when H0: Bj = aj
t = estimate - hypothesised value
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Standard error
Log - level level quadratic
(B1hat + 2B2hat x Xbar) x 100
When the question talks about goodness of fit
R^2 values
Affect of rescaling
All parameters are divided or multiplied by the change in the measurement. SO is the SSR
However the R^2 is exactly the same as the proportion
Partialling out approach
- Regress X1 on X2 to obtain residuals
- Regress y on residuals to obtain B1
What does partialling out show
That you get the same result for the multivariate regression even when taking out the effect of other variables
