|| Refreshing the statistical tools for business analytics

51. Refreshing the statistical tools for business analytics

• Kurtosis is really a measure of the outliers (tails) of the distribution. Kurtosis is really a measure of the outliers (tails) of the distribution. ... Low kurtosis, rather than being a measure of “flatness,” indicates a distribution that is less outlier-prone than is the normal distribution
• Standard deviation / variance to the mean
• 1 standard deviation is 68%
• 2 standard deviation is 95.5%
• 3 standard deviation is 97%
• Covariance measures the degree to which the two variables move together, eg. age and income
• Sum((X-mean X) (Y-mean Y)) / (n-1)
• R, the correlation coefficient measures the strength of the linear relationship between two variables
• Sum((X-mean X) (Y-mean Y)) / Square of ((Sum(X-mean X)^2 * Sum(Y-mean Y)^2)
• R close to zero, no correlation
• Regression analysis is a set of processes to estimate the relationships amongst variables
• Random error in linear regression after intercept and slope
• = Actual - estimated using the linear regression
• Types of regression
• linear regression, most common in business analysis
• logistic regression, most common in business analysis
• polynominal regression
• stepwise regression
• ridge regression
• lasso regression
• elastic net regression
• ANOVA, analysis of variance
• SST, total sum of squares, Sum (actual y - mean of y)^2
• SSE, total of sum of error, Sum (actual y - estimated y)^2
• SSR, total of sum of regression, Sum (estimated y - mean of y)^2
• SST = SSR + SSE
• Standard error of estimate SEE = square (MSE) = square (SSE / N-2)
• R squared = explained variation / total variation 
• F test measures how well the dependent variable is explained by the independent variables collectively 
• MSR, MSE, N (number of observations), K (number of independent variables)
• Decisioning rules
• reject null hypothesis if F statistics > critical value
• Weight of evidence
• Log (distribution of good/distribution of bad)
• Information value
• Sum ((DG-DB)*WOE)
• VIF, multiple variable