Last Minute Flashcards
What probability formula is used for marginal and joint probability tables
P(A|B) = P(A n B) / P(B)
What is a marginal and joint probability table
A table showing the probabilites for all combinations of 4 different variables and the probability for the totals
What can be used when working out n amount chosen from r
nCr
What is Bayes Rule
P(A|B) = P(B|A) * P(A) / P(B)
What is the formula for binomial
- P(X = k)
- (n! / k! * (n-k)!) * p^k * q^n-k
What is the formula for the poisson
- P(X = k) = e^-lambda * lambda^k / k!
What is the z test statistic for hypothesis testing (population)
z = x bar - mu / sigma / root(n)
what is the t test statistic for hypothesis testing (sample)
t = x bar - mu / s / root n
What is the formula for Bias
- Bias(theta hat) = E(theta hat) - theta
When is one estimator said to be more efficient than the other
- Var(theta 1 hat) < Var(theta 2 hat) then theta 1 hat is more efficient
- whichever one is less
How is the relative efficency of two estimators calculated
- With respect to is key
- whichever estimator it is in respect to, this estimator is on top
- Var(theta 1 hat) / Var(theta 2 hat)
What is the mean of the sampling distribution s^2
- σ^2
What is the formula for the chi squared test statsitc
chi square = (n-1) * s^2 / σ^2
How is the t value calculated for testing if a coefficient is significant in regression
- t = coefficient / standard error
What is the formula for the exponential distribution
- f(t) = lambda * e^-lambda * t
When would a finite population coefficient be used
- When n is not a small fraction of N
- N - n / n - 1
- applied to variance
How is TSS calculated
- TSS = RSS + ESS
What is key about RSS
- It is the explained variation in variable A by variable B
How is the coefficient of determination calculated
- R^2 = RSS / TSS
What is the hypothesis for a coefficient significance test
- H0: Hypothesised slope = 0
- H1: Hypothesised slope /= 0
How is the F-test and t-test related
- F = t^2
What is the formula for an overall test of significance
- F = (RSS / k) / (ESS / n-K-1)
- Reject H0 if F > F(k numerator degrees, n-k-1 denomiator degrees, aplha)
What is the hypothesis for overall significance
H0: All coefficients = 0
H1: at least one coefficient is not 0
What is the F statisitc for a subset of coefficients
- F = ((ESS(r) - ESS) / r) / (ESS / n-k-r-1)
- r is the number of excluded variables
