Statistics Formula Sheet - Regression

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REGRESSION
1. Prediction Equation

2. Sample Slope

SSx= ∑ x2- (∑ x)2/n
SSxy= ∑ xy- ∑ x*∑ y/n
3. Sample Y Intercept

4. Coeff. Of Determination

5. Std. Error of Estimate

6. Standard Error of 0 and
1

7. Test Statistic

8. Confidence Interval of 0 and 1

9. Confidence interval for mean value of Y given x

10. Prediction interval for a randomly chosen value of Y given x

11. Coeff. of Correlation

12. Adjusted R2

13. Variance Inflation Factor

14. Beta Weights

15. Partial F Test

SSER - sum of squares of error of reduced model SSEF - sum of squares of error of full model r – no. of variables dropped from full model.

16. Outliers
Measure | Potential Outliers |
Standardized residual, Studentized residual | > 3 (3 sigma level) | Mahalanobis distance | > Critical chi-square value with df = number of explanatory variables(Outliers in independent variable) | Cook’s distance | > 1 implies potential outlier |

Leverage values | > 2(k+1)/n, then the point is influential (k is the number of independent variables and n is the sample size) | SDFBeta | > 2/n |
SDFFit | |
17. Mahalanobis Distance
Mi = (Xi – X)2/ Sx
18. Cook’s Distance
Di =
∑j (Yj – Yj(i))2/k x MSE
19. Durbin Watson Test
Durbin Watson value close to 2 implies no auto-correlation
Durbin Watson value close to 0 implies positive auto-correlation Durbin Watson value close to 4 implies negative auto-correlation 20. Relationship between F and R2
F = (R2/1- R2) x ((n-(k+1))/k)
FORECASTING
1. Exponential Smoothing

2. Double Exponential Smoothing

3. Theil’s Coeff

U1 is bounded between 0 and 1, with values closer to zero indicating greater accuracy. If U2 = 1, there is no difference between naïve forecast and the forecasting technique If U2 < 1, the technique is better than naïve forecast

If U2 > 1, the technique is no better than...
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