Polynomial Regressions

Which of the following statements are true?

I. A regression equation with k independent variables has k regression coefficients.

II. Regression coefficients (bo, b1, b2, etc.) are variables in the regression equation.

III. The principle of least squares calls for minimizing the sum of the squared residuals.

• I only.

• II only.

• III only

• All of the above

• None of the above.

Which one of the statement is true regarding residuals in regression analysis?

• Mean of residuals is always zero

• Mean of residuals is always less than zero

• Mean of residuals is always greater than zero

• There is no such rule for residuals.

Which of the following step / assumption in regression modeling impacts the trade-off between under-fitting and over-fitting the most.

• The polynomial degree

• When we learn the weights by matrix inversion or gradient descent

• The use of a constant-term

A Polynomial provides the best approximation of the relationship between the dependent and independent variable.

• TRUE

• FALSE

For the polynomial regression model,

• you need new estimation techniques since the OLS assumptions do not apply any longer.

• the techniques for estimation and inference developed for multiple regression can be applied.

• you can still use OLS estimation techniques, but the

  t-statistics do not have an asymptotic normal distribution.

• the critical values from the normal distribution have to be changed to nth power