Correlation & Regression Analysis PDF

Correlation Analysis Correlation doesn't imply causation Correlation Analysis ​ Correlation analysis: Measures the strength of the linear relationship between 2 variables ​ Pearson Correlation Coefficient (r) ○​ Measure the degree of Linear association between two continuous...

Correlation Analysis Correlation doesn't imply causation Correlation Analysis ​ Correlation analysis: Measures the strength of the linear relationship between 2 variables ​ Pearson Correlation Coefficient (r) ○​ Measure the degree of Linear association between two continuous variables (x and y) ​ Population correlation (p) or sample correlation r lies between -1 and 1 ○​ Values on the left side of the scale means negative ​ Therefore when one variable decrease the other increases ○​ Positive on the right side ​ Variables on the right side mean variables go up together or down together ○​ If sample correlation (r ) or population correlation P is equal to 0, then there is absence of linear association  ​ ○​ Called scatter plots ​ Scatter Plots ​ What is considered weak or strong correlation effect size ○​ Weak correlation effect +- 0.1 ○​ Moderate correlation effect +- 0.3 ○​ Strong correlation effect +- 0.5 Correlation Analysis Example  ​ ​ We can not state there is a independent variable or dependent variable ​ We can not state there is a direction between one variable for another just correlation ​ We cannot study directionality meaning we do not hypothesize a case effect direction Regression Analysis ​ Even a regression analysis can measure only the nature and degree of association or (covariation) between variables ​ To establish causation, along with mathematical models (regression), one needs underlying knowledge, theories and accounting for confounders ​ Regression analysis: Statistical Technique used to related two or more variables ○​ The goal is to create a regression model that relates one or more independent variable (IV) to the effect or change of the dependent variable (DV) ○​ The independent variable can be either continuous or categorical, But, the DV can only be a Continuous variable  ○​ We use regression analysis to explain and predict the variable of interest, the dependent variable ​ Applications of Regression Analysis ○​ How does word of mouth impact sales of boxed wine? ○​ Whether and how do cross promotions and pricing impact the use of Amazon’s videos streaming service ○​ Is the effect of advertising on brand equity for Costco different for traditional vs digital media? Regression Equations ​ Simple Linear Regression: when only one independent variable in the model (X variable) ​ One one X represent the IV -​ Can only have 1 beta 1 B1, because there is only one IV -​ Coefficient, the estimated parameter that goes together with the variable ​ Multiple ,linear regression when there is more than one independent variable (more than one X variable) ​ There are multiple Xs meaning multiple IV Interpreting the Regression Parameters Testing Significance of Regression Parameters ★​ If beta coefficient is 0, there is no effect of X and Y ★​ If beta coefficient is significant different than 0, then there was an effect of x and y ​ SImple linear regression Model -​ If beta is no equal to there then, X (IV) is impact Y in the simple linear equation model ​ Multiple Linear Regression Model -​ Instead of only having one X, we have multiple IV,  -​ Therefore we have one coefficient parameter (Beta) for each Independent variable and we need to test of each of them -​ For null hypothesis : beta is = 0 -​ Alternative hypothesis: not all betas are equal to zero ➔​ There is at least one beta coefficient not equal to 0 ​ Remember we always want lower p-values Coding Categorical Variables ​ Only 2 categorical variables ​ Multiple categorical variables -​ I have 3 categories, and i need to create a dummy variable -​ We code n-1 categories ➔​ 3-1= 2, so we can only create 2 dummy variables and 1 will be chosen as the baseline ➔​ Heavy user will be the baseline, became there is a row of 0s ➔​ Light user and moderate use will be the dummy each one has a 1 and 0, not a double zero like in heavy user Simple Regression Analysis Example ​ Regression equation explanation ○​ Recommendation= Beta zero( the intercept) + plus Beta one, related to variable satisfaction + error Multiple Regression Analysis Example -​ When all the IVs, equal 0, the mean/average level of satisfaction is equal to 2.5 (when nothing is influencing the dependent variable -​ Beta 5, regarding the service: customer satisfaction increases by 2.5 units when “services increase by 1 unit  -​ This was measured as not continuous, it was measured by categorical Interpreting a Regression Output ​ Overall summary ​ Regression Statistics ○​ How well the regression model applies to the data we have at hand ○​ R Square: Measure of model fit. This is how well the model fits the data ​ R square ranges between 0-1, closer to one means the better the fitting model  ​ Base on the table we have.94, means that 94% of the variance on the dependent variable (Y) is explained by the independent variables (Xs) ○​ Adjusted r-square: is the better metric, bc is accounts for shared variance ○​ Adjusted r square and r-square should be the same ​ ANOVA ○​ F: F Statistic test, tests whether having a regression models for HA (alternative hypothesis) is better than having a null model (HO) ○​ Significance F (is the P-Value): As a p-value related to F test is