Statistics Formula Sheet - Regression
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
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