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when might overfitting occur - when the # of factors is close to or larger than the # of data
points causing the model to potentially fit too closely to random effects
Why are simple models better than complex ones - less data is required; less chance of
insignificant factors and easier to interpret
what is forward selection - we select the best new factor and see if it's good enough (R^2, AIC,
or p-value) add it to our model and fit the model with the current set of factors. Then at the end
we remove factors that are lower than a certain threshold
what is backward elimination - we start with all factors and find the worst on a supplied
threshold (p = 0.15). If it is worse we remove it and start the process over. We do that until we
have the number of factors that we want and then we move the factors lower than a second
threshold (p = .05) and fit the model with all set of factors
what is stepwise regression - it is a combination of forward selection and backward elimination.
We can either start with all factors or no factors and at each step we remove or add a factor. As
we go through the procedure after adding each new factor and at the end we eliminate right
away factors that no longer appear.
,what type of algorithms are stepwise selection? - Greedy algorithms - at each step they take
one thing that looks best
what is LASSO - a variable selection method where the coefficients are determined by both
minimizing the squared error and the sum of their absolute value not being over a certain
threshold t
How do you choose t in LASSO - use the lasso approach with different values of t and see which
gives the best trade off
why do we have to scale the data for LASSO - if we don't, the measure of the data will artificially
affect how big the coefficients need to be
What is elastic net? - A variable selection method that works by minimizing the squared error
and constraining the combination of absolute values of coefficients and their squares
what is a key difference between stepwise regresson and lasso regression *** - If the data is not
scaled, the coefficients can have artificially different orders of magnitude, which means they'll
have unbalanced effects on the lasso constraint.
Why doesn't Ridge Regression perform variable selection? - The coefficients values are squared
so they go closer to zero or regularizes them, but the coefficient values are never equal to zero
What are the pros and cons of Greedy Algorithms (Forward selection, stepwise elimination,
stepwise regression) - Good for initial analysis but often don't perform as well on other data
because they fit more to random effects than you'd like and appear to have a better fit
What are the pros and cons of LASSO, Ridge and Elastic Net - They are slower but help make
models that make better predictions
, Which two methods does elastic net look like it combines and what are the downsides from it? -
Ridge Regression and LASSO.
Advantages: variable selection from LASSO and Predictive benefits of Ridge.
Disadvantages: Arbitrarily rules out some correlated variables (e.g. LASSO doesn't know which
one should be left out); Underestimates coefficients of very predictive variables (i.e. Ridge
Regression)
What are some downsides of surveys? - Even if you have what appears to be a representative
sample in simple ways, maybe it isn't in more complex ways.
If we're testing to see whether red cars sell for higher prices than blue cars, we need to account
for the type and age of the cars in our data set. This is called: - Controlling
what is a blocking factor *** - a source of variability that is not of primary interest to the
experimenter
what is an example of a blocking factor - The type of car, sports car or family car, is a blocking
factor that it could account for some of the difference between red cars and blue cars. Because
sports cars are more likely to be red; if we account for the difference, we can reduce the
variability in our estimates
Under what conditions should you run A/B tests - When you can collect data quickly. When the
data is representative and the amount of data is small compared to the whole population
Do you have to decide the sample size ahead of time for A/B tests - no, and we can run the
hypothesis test anytime we want