What is the coefficient of determination ?
It estimates the fraction of the variance in Y that is explained by X.
Always between 0 and 1.
What is the regression analysis ?
The regression analysis is a set of empirical methods designed to estimate the relationships between variables, as defined in an equation model.
We use it to test the theories that predict these relationships.
Can you give some example of regression analysis ?
Ex :
Theory : wage = f(education, experience)
Model: wage = Bo(date 0) + B1 education + B2experience + e
What is B0 in the regression analysis ?
B0 is the ‘constant’ of the model, here the wage with no education and no experience
What is “e” in the regression analysis ?
“e” is the error term or disturbance.
“e” contains the unobserved factors and the measurement errors.
What is the “ei” ?
Epsilon (ei) = the actual value for Y (Yi) - the predicted value for Y(Y chapeau i)
What is OLS ?
OLS = Ordinary least squares regression
What is R² ?
R² = explained variation in Y = total variation in Y.
What is a good R² ?
It depends, if your goal is to , R = 1 is better.
if your is to look at the impact of the variable, you don’t care about R².
What is the similarities between correlation and regression ?
- 3 similarities :
the standardized regression coefficient is the same as Pearson’s correlation coefficient
• The square of Pearson’s correlation coefficient is the same as theR2in simple linear regression
• Neither simple linear regression nor correlation answer questions of causality directly.
- 3 similarities :
When do you reject your correlation hypothesis ?
If p is inferior as a, usually 5% is significant. Than you rejected the non-hypothesis, there is an effect.
If p value is greater than 5% you failed to and you rejected to. Than you accepted the hypothesis.
What are the step ?
Look at model fit. If the p-value of the F-test H0 : model does not explain a significant amount of Y variation.
What is the difference between multiple R² and adjusted R² ?
Multiple R² = just goes up so
Adjusted R² is the proportion of Y that you explain.
What is a multiple regression analyisis ?
Multiple regression is a statistical approach used to quantify the sign and magnitude of the relationship between a focal dependent variable (marketing outcome in our context) and several independent variables (e.g., marketing effo
When do you have to use a multiple regression analysis ?
- To determine how one of multiple marketing interventions incrementally affects observed marketing outcomes.
- To compare the effects of multiple marketing interventions on marketing outcomes.
- To predict the likely market outcomes due to various combinations of marketing interventions
Is cross elasticity are negative or positive ?
It depends :
Complementary -> negative
if it is the concurrents products -> it is positive
How many IVS should you include ?
Each variable should :
- Have a theoretically plausible reason
- Add explanatory power
- Can not highly correlate with any other independent variable
What is a directional hypothesis ?
If X goes up, Y goes up, it’s a directional hypothesis
If X goes up, Y goes down, it’s a directional hypothesis.
If X goes up, Y goes I don’t know, it’s not a directional hypothesis.
What is the difference between prediction and prescription analysis ?
Last slide.
