The exhaustive list of topics in Regression Analysis in which we provide Help with Homework Assignment and Help with Project is as follows:
- Need for statistical analysis, Straight line relationship between two variables. SIMPLE LINEAR REGRESSION: fitting a straight line by least squares.
- Useful properties of Least squares fit, Statistical properties of least squares
estimators, Analysis of Variance
- Confidence intervals and tests for ß0 and ß1. F-test for significance of regression. The correlation between X and Y .
- Interval estimation of the mean response, Prediction of new observation.
Coefficient of determination.
- MULTIPLE LINEAR REGRESSION, Estimation of model parameters. Properties of least squares estimators.
- Hypothesis testing in multiple linear regression, Analysis of variance, Test for significance of regression, Tests on individual regression coefficient.
- Extra sum of squares method and tests for several parameters being zero,The extra sum of squares principle, Two alternative forms of extra SS, Two predictor variables: Example.
- Multiple regression-Special topics: Testing a general linear hypothesis.
- Confidence intervals in multiple regression: Confidence intervals on the regression coefficients, Confidence interval estimation of mean response,
Prediction of new observations.
- EVALUATING THE PERFORMANCE OF A REGRESSION MODEL, Residual Analysis: Method for scaling residuals, Standardized residuals, Studentized residuals, PRESS residuals.
- Residual plots: Normal probability plot, Plot of predicted response (^y) against observed response (y), Plot of residuals (ei) against fitted values
(^y). Partial residuals plot.
- Serial correlation in residuals, The Durbin-Watson test for a certain type of serial correlation.
- Examining Runs in the time sequence plot of residuals: Runs test.
- More on checking fitted models, The hat matrix H and the various types of residuals. Variance-covariance matrix of e, Extra sum of squares attributable to ei.
- DIAGNOSTICS FOR LEVERAGE AND INFLUENCE, Detection of influential observations: Cook’s D,DFFITS and DFBETAS.
- POLYNOMIALREGRESSIONMODELS,Polynomial models in one variable: Example.
- Picewise Polynomial Fitting (splines), Example: picewise linear regression.
- Orthogonal polynomials regression.
- Models containing functions of the predictors,including polynomialmod-els,Worked examples of second- order surface fitting for k=3 and k=2 predictor variables.
- TRANSFORMATIONS AND WEIGHTING TO CORRECT MODEL INADEQUA-CIES.Variance-stabilizing transformations,Transformations to linearize the model.
- Analytical methods for selecting a transformation.Transformations on y: TheBox-CoxMethod, Transformations on the regress or variables.
- Generalized least squares and weighted least squares.An example of weighted least squares,A numerical example of weighted least squares.
- DUMMY VARIABLES: Dummy variables to separate blocks of data with different intercepts, same model.
- Interaction terms involving dummy variables, Dummy variables for segmented models.
- SELECTING THE BEST” REGRESSION EQUATION. All possible regressions and “Best subset” regression.
- Forward Selection, Stepwise Selection, Backward elimination, Significanc levels for selection procedures.
- MULTICOLLINEARITY: Sources of multicollinearity, Effects of multicollinearity.
- Multicollinearity diagnostics: Examination of the correlation matrix, Variance Inflation Factors, Eigen system Analysis of X'X.
- Methods for dealing with multicollinearity: Collecting additional data,Re-move variables from the model,Collapse variables.
- Ridge regression: Basic form of Ridge Regression, In what circumstances is ridge regression absolutely the correct way to proceed?.
- GENERALIZED LINEAR MODELS (GLIM): The exponential family of distributions: examples
- Logistic regression models: models with binary response variable.Estimating the parameters in alogistic regression model,Interpretation of the parameters in logistic regression model,Hypothesis tests on model parameters.
- Generalized Linear Models (GLIM): Link functions and linear predictors, Parameter estimation and inference in the GLM.
- NON LINEAR ESTIMATION,Linear regression models,Non linear regression models,Least squares for non linear models.
- Estimating the Parameters of a non linear systems,An example.
- Robust Regression:Least absolute deviations regression(L1regression),M-estimators,Steelemploymentexample.
- Least median ofsquares regression,Robust regression with ranked residuals.
- EFFECT OF MEASUREMENT ERRORS INREGRESSORS:Simple linear regression,The Berkson Model.
- INVERSE ESTIMATION-The calibration problem.
- Resampling procedures(BOOTSTRAPPING):Resampling procedures for regression models,Example:Straight line fit.