Question

1) Which is NOT a fundamental assumption of OLS (Ordinary Least Squares)?

a)       The regression model is nonlinear in the coefficients and error term.

  b)       Observations of the error term are uncorrelated with each other.

   c)    No independent variable is a perfect linear function of any other explanatory variables.

   d)   The error term has homoscedasticity.

e)   All independent variables will be uncorrelated with the error term.

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2) You test a model that yields a high training Mean Squared Error. Which of the following is correct?

a)       Due to the nature of the MSE metric, the test MSE will be similarly high.

b)       The variance of the error terms in the test MSE calculation will be reducible.

c)       The MSE calculation for the test data will not include the squared bias.

d)       Interaction terms need to be added to the model.

e)       There is no guarantee that the test MSE will be high.

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3) What does it mean when we say that forward and backward stepwise selection algorithms are greedy?

a)       They increase the R-squared at the expense of adding redundant variables.

b)       They coerce the parameter coefficients downwards.

c)       They only take the best step forward at each selection stage and may not end up with the best model.

d)       They often increase the heteroscedasticity of the model while trying to reduce its bias.

e)       They will often find the best model but will end up significantly increasing both the bias and variance.

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4) Which of the following statements is true regarding the tuning parameter in Lasso regression?

a)       When the tuning parameter increases, bias decreases.

b)       As the tuning parameter increases, fewer and fewer variables/parameters will be removed.

c)       When the tuning parameter decreases, variance decreases.

d)       When the tuning parameter equals zero, no variables/parameters will be removed.

e)       None of the above

Answer 1

The statement that is NOT a fundamental assumption of OLS (Ordinary Least Squares) :

• a) The regression model is nonlinear in the coefficients and error term.

One test a model that yields a high training Mean Squared Error. The statement that is correct :

• e) There is no guarantee that the test MSE will be high.

The meaning when we say that forward and backward step wise selection algorithms are greedy :

• They will often find the best model but will end up significantly increasing both the bias and variance.

The following statement that is true regarding the tuning parameter in Lasso regression :

• d) When the tuning parameter equals zero, no variables/parameters will be removed.