Click to edit Master title style Regression: Independent and Dependent Variables.
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Transcript of Click to edit Master title style Regression: Independent and Dependent Variables.
Regression:Regression:Independent Independent
and Dependent and Dependent VariablesVariables
Euro Cup Round 4(Final Results)
1. From the Homeworks page.
2. Do at least 1 ANOVA problem and at least 1 Regression problem by the end of class.
In-Class Activity(Due By: 5pm today)
• Go to Homeworks page, select Survey 2.
• Answer the 10 simple rating questions for the four familiar characters.
• Pay attention to the questions and your answers – there are attention checks…
Applications ofMultiple Regression
Forecasting:
Weather
Sales
Stock prices
Dating Services
Rating Responses:
What is your major?
How much money do you want to make?
Is religion important to you?
Do you prefer video games over movies?
Are you looking for a serious relationship?
Are you a morning person or a night person?
Dependent Variable: Length of relationship.
r R2 R2
-1.0 1.0 100%
-0.9 0.81 81%
-0.75 0.56 56%
-0.5 0.25 25%
-0.25 0.06 6%
0 0 0%
0.25 0.06 6%
0.5 0.25 25%
0.75 0.56 56%
0.9 0.81 81%
1.0 1.0 100%
One Predictor Variable
2 || Rr
Issues
Adding predictor variables: overfitting (or, “fitting the noise”) and cross-validation.
Mood ≈ Mood in this dataset(Approx. = )
Scatterplot
One Predictor VariableSimple (Linear) Regression
Perfect Fit, R2 = 100% !
Horrible Prediction!
Adding predictor variables to your model gives the model more flexibility.
The model can (and will) always ignore a predictor if it doesn’t help improve the fit to available data.
So, adding a predictor variable CANNOT cause R2 to decrease. R2 will almost always INCREASE, even if the predictor is NOT correlated to the Dependent Variable.
The penalty for adding useless predictors to your model will come when you use the fitted model to PREDICT NEW datapoints.
What’s Going On?
Check the p Value for the coefficient of the predictor in the Regression Table. It should be ‘small’ (e.g., less than 0.05).
Cross Validation Test: Use half of your dataset to fit the model. Use the other half to see how good you can PREDICT new data.
Compare “Adjusted R Square” values for models with and without that predictor.
How Do Know if a Predictor is‘Fitting to Noise’?
Issues
Adding predictor variables: overfitting (or, “fitting the noise”) and cross-validation.
Multicolinearity. Predictor variables are correlated among themselves (NOT a good thing!).
Miles Per Gallon Predicts Tank Size
Kilometers Per Gallon Predicts Tank Size
Kilometers AND Miles Per Gallon do NOT predict Tank
Size?