Linear Regression Analysis 5th edition Montgomery, Peck & Vining

1.1 Regression and Model Building Regression analysis is a statistical technique for investigating and modeling the relationship between variables. Equation of a straight line (classical) y = mx +b we usually write this as y = 0 +1x Linear Regression Analysis 5th edition Montgomery, Peck & Vining

1.1 Regression and Model Building Not all observations will fall exactly on a straight line. y = 0 + 1x +  where  represents error it is a random variable that accounts for the failure of the model to fit the data exactly.  ~ N(0, 2) Linear Regression Analysis 5th edition Montgomery, Peck & Vining

1.1 Regression and Model Building Delivery time example Linear Regression Analysis 5th edition Montgomery, Peck & Vining

1.1 Regression and Model Building Simple Linear Regression Model where y – dependent (response) variable x – independent (regressor/predictor) variable 0 - intercept 1 - slope  - random error term Linear Regression Analysis 5th edition Montgomery, Peck & Vining

Linear Regression Analysis 5th edition Montgomery, Peck & Vining

1.1 Regression and Model Building The mean response at any value, x, of the regressor variable is The variance of y at any given x is Linear Regression Analysis 5th edition Montgomery, Peck & Vining

Linear Regression Analysis 5th edition Montgomery, Peck & Vining

Linear Regression Analysis 5th edition Montgomery, Peck & Vining Figure 1.3 Linear regression approximation of a complex relationship. Linear Regression Analysis 5th edition Montgomery, Peck & Vining

Linear Regression Analysis 5th edition Montgomery, Peck & Vining Figure 1.4 Piecewise linear approximation of a complex relationship. Linear Regression Analysis 5th edition Montgomery, Peck & Vining

Linear Regression Analysis 5th edition Montgomery, Peck & Vining Figure 1.5 The danger of extrapolation in regression. Linear Regression Analysis 5th edition Montgomery, Peck & Vining

1.1 Regression and Model Building Multiple Linear Regression Model Linear Regression Analysis 5th edition Montgomery, Peck & Vining

Linear Regression Analysis 5th edition Montgomery, Peck & Vining 1.2 Data Collection Your analysis/model is only as good as the data Three different methods can be used for data collection A retrospective study based on historical data An observational study A designed experiment Linear Regression Analysis 5th edition Montgomery, Peck & Vining

Linear Regression Analysis 5th edition Montgomery, Peck & Vining 1.2 Data Collection Linear Regression Analysis 5th edition Montgomery, Peck & Vining

Linear Regression Analysis 5th edition Montgomery, Peck & Vining

Linear Regression Analysis 5th edition Montgomery, Peck & Vining

Linear Regression Analysis 5th edition Montgomery, Peck & Vining

Linear Regression Analysis 5th edition Montgomery, Peck & Vining

Linear Regression Analysis 5th edition Montgomery, Peck & Vining Designed Experiment Linear Regression Analysis 5th edition Montgomery, Peck & Vining

Linear Regression Analysis 5th edition Montgomery, Peck & Vining 1.3 Uses of Regression There are many uses of regression, including: Data description Parameter estimation Prediction and estimation Control Regression analysis is perhaps the most widely used statistical technique, and probably the most widely misused. Linear Regression Analysis 5th edition Montgomery, Peck & Vining

Linear Regression Analysis 5th edition Montgomery, Peck & Vining 1.3 Uses of Regression Cause and Effect Relationships Caution: just because you can fit a linear model to a set of data, does not mean you should. It is relatively easy to build “nonsense” relationships between variables Regression does not necessarily imply causality Linear Regression Analysis 5th edition Montgomery, Peck & Vining

Model building in regression Linear Regression Analysis 5th edition Montgomery, Peck & Vining