Quantitative Analysis and Decision Methods Formulas Essay Example

Quantitative Analysis and Decision Methods Formulas Essay Example Quantitative Analysis and Decision Methods Formulas Essay Quantitative Analysis and Decision Methods Formulas Essay Quant Formula Study Guide MISCELLANEOUS, COMMONLY USED FORMULAS Finite population correction factor: Multiply SE of sample mean by fpc to make the correction - Independent samples of same population with same standard deviation (variances are equal). Confidence interval: df for t-multiple is (df1 + df2), or (n1 – 1) + (n2 1) Pooled estimate of common standard deviation: SE of difference between two sample means - Confidence interval for differences in sample means when variance is not equal. df for t-multiple is given by complex formula not shown in book when variance is not equal. Use StatTools. Confidence interval for difference between two proportions. SE for difference between two proportions. - Chapters 2 and 3 Describing the Distribution of a Single Variable and Finding Relationships among variables Mean Formula Excel Function: = AVERAGE Coefficient of Variation: Standard Deviation / Mean Standard Deviation: square root of variance Sample Variance Population Variance Excel Function: Variance = VAR Standard Deviation = STDEV Mean Absolute Deviation Covariance Correlation Excel Function: =CORREL Chapter 4: Probability and Probability Distributions Conditional probability: P(A|B) = P(A and B) / P(B) Multiplication rule: P(A and B) = P(A|B) P(B) If two events are INDEPENDENT: P(A and B) = P(A) P(B) Variance of a Probability Distribution: Standard Deviation of a Probability Distribution: Conditional Mean: * when the mean of a variable depend on an external event Covariance between X and Y: Correlation between X and Y: Joint Probability Formula: P(X = x and Y = y) = P(X = x|Y = y) P(Y = y) Alternative formula: P(X = x and Y = y) = P(Y = y|X = x) P(X = x) Joint probability formula for independent random variables: P(X = x and Y = y) = P(X = x) P(Y = y) Expected value of a weighted sum of random variables: E(Y) = a1E(X1) + a2E(X2) + †¦ + anE(Xn) Chapter 5 Normal, Binomial, Poisson, and Exponential Distributions Normal Density Function Mean Stdev Chapter 7 Sampling and Sampling Distributions Unbiased Property of Sample Mean Standard Error of Sample Mean Approximate Standard Error of Sample Mean Approximate) Confidence Interval for Population Mean Standard Error of Mean with Finite Population Correction Factor Finite Population Correction Factor Chapter 8 Confidence Interval Estimation Typical Form of Confidence Interval Standardized Z-Value Standardized Value Confidence Interval for Population Mean Point Estimate for Population Total Mean and Standard Error of Point Estimate for Population Total Approximate Standard Error of Point Estimate for Population Total Standard Error of Sample Proportion Confidence Interval for a Proportion Upper Limit of a One-Sided Confidence Interval for a Proportion Confidence Interval for Difference Between Means Standard Error of Difference Between Sample Means Confidence Interval for Difference Between Proportions Standard Error of Difference Between Sample Proportions Sample Size Formula for Estimating a Mean Sample Size Formula for Estimating a Proportion Sample Size Formula for Estimating the Difference Between Means Sample Size Formula for Estimating the Difference Between Proportions Chapter 9 Hypothesis Testing Hypothesis Test for a Population Mean: one-sample t-test P(t-valueconst)= ?. Excel functions: TDIST() and TINV() Test statistic for test of proportion: Test statistic for paired samples test of differences between means: Test statistic for independent samples test of difference between means: Standard error for difference between sample proportions: Resulting test statistic for difference between proportions: Chapter 10 Regression Analysis: Estimating Relationships Formula for Correlation: Slope in simple linear regression: Intercept in simple linear regression: Y is the dependent variable, and X1 through Xk are the explanatory variables, then a is the Y-intercept, and b 1 through bk are the slopes. Collectively, a the bs in the equation are called the regression coefficients. Standard Error of Estimate: R squared / R^2 General Linear Regression: Regression line: Sampling distribution of a regression coefficient has a t distribution with n-k-1 degrees of freedom: ANOVA total variation of a variable The part unexplained by the regression equation: The part that is explained: SSR = SST SSE Point Prediction: Standard error of the prediction for a single Y: Standard error of prediction for the mean Y: Chapter 11, Regression Analysis: Statistical Inference Population regression line joining means: ?Y|X1†¦Xk = ? + ? 1X1 + †¦ + ? kXk error a: Y = a + a1X1 + †¦ + akXk + a Regression line : Y = ? + ? 1X1 + †¦ + ? kXk + ? Sampling distribution of a regression coefficient has a t distribution with n-k-1 degrees of freedom: The ANOVA table splits the total variation of a variable: into the part unexplained by the regression equation: Standard error of prediction for a single Y: Standard error of prediction for the mean Y: Chapter 12, Time Series Analysis and Forecasting Mean Absolute Error: Root Mean Square Error: Mean Absolute Percentage Error: All forecasting models have the general form of the equation: Yt = Fitted Value + Residual ?Linear trend model is given by: Yt = a + bt + et Appropriate regression equation contains a multiplicative error term: ut: Yt = cebtut. Equation for the random walk: Yt = Yt-1 + m + et. Simple Exponential Smoothing: ? Formula: Ft+k = Lt = ? Yt + (1 – ? )Lt-1 Formulas for Holt?  ¦s exponential smoothing method: Winters’ Exponential Smoothing Method : Bayes’ Rule: Chapter 13: Introduction to Optimization Modeling No formulas there..