# Statistics Formula Sheet - Regression

**Topics:**Regression analysis, Normal distribution, Studentized residual

**Pages:**3 (390 words)

**Published:**October 23, 2012

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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