Quantitative Methods Flashcards

1
Q

Covariance

A

SUM[(Xbar-Xi)*(Ybar-Yi)] / (n-1)

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2
Q

Correlation Coefficient

A

r = Cov(x,y) / [Sigma(x)*Sigma(y)]

where, -1 < r < 1

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3
Q

T-test

A

t = [r * sqrt(n-2)] / sqrt(1-r^2)

Reject H0 if t+critical < t or t-critical>t.
t needs to be in between the two critical t’s

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4
Q

Slope of regression line

A

b1 = Covariance / Variance

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5
Q

Total Sum of Squares (SST)

A

SUM(Yi - Ybar)^2

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6
Q

Sum of Squared Errors (SSE)

A

SUM(Yi-Yhat)^2

This is the unexplained variation in the regression

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7
Q

Regression Sum of Squares (RSS)

A

SUM(Yhat-Ybar)^2

This is the explained variation in the regression

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8
Q

Total Variation = Explained Variation + Unexplained Variation

A

SST = RSS + SSE

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9
Q

Mean Regression Square of Sums (MSR)

A

=RSS/number of slope parameters

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10
Q

Mean Squared Error (MSE)

A

MSE = SSE / (n-2)

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11
Q

Regression degree of freedom = k
Error degree of freedom = n - k - 1

Where k = number of slope parameters

A

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12
Q

R^2 = (SST - SSE) / SST = RSS / SST

A

R^2 = (Total Variation - Unexplained Variation) / Total Variation = Explained Variation / Total Variation

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13
Q

Standard Error of the Estimate (SEE)

A

SEE = SqRt (MSE) = SqRt(SSE/(n-2))

Smaller SEE means the regression has better fit

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14
Q

F-Test tests the statistical significance of a regression

A

F = MSR / MSE = (Rss/k)/(SSE/[n-k-1])

Always a one tail test

Reject if F > Fcritical

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15
Q

F-test hypothesis testing

A
  1. H0 –> b1=b2=b3=b4=0 vs. Ha–> @ least 1 bi is not =0
  2. Decision —> Reject H0 if F(test-statistic) > Fcritical
  3. If rejected, Bj is significant
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16
Q

Adjusted R^2

A

Ra^2 = 1 - {[(n-1)/(n-k-1)]*(1-R^2)}

17
Q

t = coefficient / standard error

18
Q

Breusch Pagan Chi-Square Test is used to detect heterskedasticity

A

ChiSquare = n * R^2residuals
with k degrees of freedom.

To correct heteroskedasticity, calculate the robust standard errors.

19
Q

Durbin-Watson Statistic is used to detect serial correlation (residual terms are correlated with each other)

A

DW = SUM[(EtHAT - Et-1HAT)^2] / SUM(EtHAT^2)

Decision Rule:
Dw < dl reject null, positive serial correlation
dl du fail to reject null, no evidence of serial correlation

20
Q

Use the Hansen method to correct for serial correlation

21
Q

Detect Multicollinearity 1. t-test says no variable is statistically significant, and 2. F-test is statistically significant and R^2 is high.

A

Correct multicollinearity by omitting highly correlated variables

22
Q

Log-Linear Models

A
Yt = e^(b0+b1(t)) --->
ln(Yt) = b0 + b1(t)
23
Q

Autoregressive Models

A

Xt = b0 + b1Xt-1 + b2Xt-2+…+bpXt-p + ErrorTerm

24
Q

Chain rule of forecasting

A
Xt+1 = b0 + b1*Xt
Xt+2 = b0 + b2*Xt+1
25
T-test
t = correlation of error terms / [1/SqRt(T)] with T-2 degrees of freedom. If the test is rejected, add more lag variables and re-test
26
Mean Reverting Level is the tendency to move back to the mean
Xt = b0/(1-b1)
27
Dickey Fuller Test
1. Xt = b0 + b1*Xt-1 + Error 2. Xt - Xt-1 = b0 + (b1-1)*Xt-1 + Error 3. Test the (b1-1) term using the t-test. If it is rejected, there is no unit root. A unit root is when a time series is not covariance stationary.
28
Auto Regressive Conditional Heteroskedasticity (ARCH) exists if the variance of the residuals in one period is dependent on the variance of the residuals in a previous period.
Errort^2 = A0 + A1*ErrorT-1^2 + Sigmat
29
Variance of ARCH series
Sigmat+1^2 = A0 + A*Errort^2