Stat Final Cheat Sheet
1. 2- Multiple regression
a. Equation
b. Meaning of coefficients - for a given x2, for each additional unit of x1
c. Slopes
d. r^2
e. Coefficients of partial determination
f. 95% CIE, PIE
g. Does each independent variable contribute to the model?
i. X1: 95% CIE for B1 → b1-(tcritical)(Sb1) ≤ B1 ≤ b1+(tcritical)(Sb1) - so if
0 is not in the interval, we can say it contributes to model
ii. Or use tsat- Ho: no linear relationship between Y and X1; Ha: There is a
relation between Y and X1 - Tstat>Tcrit= reject Ho
h. Multiple regression - a significant relationship between Y and two X variables
i. Ho: no relationship, Ha: is a relationship→ Fstat vs. Fcritical
2. 3- Logistic Regression
a. Equation (ln odds = y)
b. Meaning of coefficients - holding constant the effects of X2, for each increase in
X1, ln(odds) increases by [x1 coefficient]
c. With equation, find Odds ratio and probability
d. Is there evidence that this logistic model uses X1 and X2 to determine Y?
i. Deviance Test (used to compare models)
1. Ho: No difference between model predictors and reality (the model
is a good fitting model); Ha: There is a significant difference
[Model not good] → Deviance > X2 Critical = Reject Ho.
e. Is there evidence that x1 and x2 EACH make impact on logistic model? →
WALDS test for individual slopes
i. Ho: B1=0, Ha; B1 ≠ 0 → Zstat>Zcrit = reject Ho. They contribute
3. 4- Mean cost of Y in multiple X
a. Is there evidence that there is a difference in Y(mean costs) of import across X(4
regions)?
i. Ho: No SD between cost to import for 4 regions; Ha: There is a Diff →
Fstat>Fcrti = Reject Ho. Now can do Tukey Procedure to find which
regions differ in mean
b. Is there evidence of a difference in variation in Y(cost to import) among (4
regions)?
i. Ho: No SD between variation of Y in X; Ha: Is a SD of Y in X →
Fstat>Fcrit = Reject Ho.
c. Take the region with the lowest mean costs as the optimal location
4. 5- Interaction
a. Is there interaction between Factor A & B? (2 way anova)
i.
Ho: no interaction = independent. Ha: Yes interaction → Fstat<Fcrit from
interaction row = dont reject Ho, factors independent. If yes interaction =
END
b. Effect due to Factor A?
i. Ho: no SD in Y between/caused by Factor A types. Ha: Yes SD →
Fstat<Fcrit from Factor A(sample) row → cant reject Ho → END
1. If I reject Ho→ Proceed with Tukey
c. Tukey?
Df
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Multiple regression table
Mean cost of y acriss x
Adjusted R^2
1- [(Total DF/Error DF) * (Error SS/Total SS)]
Logistics
- Zstat = COefficent / SE coefficient
C= Number of group - so lets say groups asia, africa, eurpoe, north ameria, C= 3
0
