Format

The midterm will be comprehensive. Review the lecture notes and handouts. The exam will be ninety minutes but it is possible to complete all questions in less than sixty minutes.

Each question may be divided into two sections.

• Computational/Technical:

  Make sure that you can do the following:

  • Derive estimates of the coefficients of the simple linear regression equation using least squares.
  • Use Matrix Algebra to determine the vector b.
  • State the Hat Matrix and show how it may be used to derive the residual vector e.
  • Compute the determinant of 2x2 and 3x3 matrices.
  • Compute the length of a vector.
  • Show that two vectors are perpendicular.
  • Express the characteristic equation of a matrix as a polynomial.
  • Derive the eigenvalues and eigenvectors of a 2x2 matrix.

• Discussion/Descriptive:

  Be prepared to discuss basic concepts and terminology. You may be asked to "discuss" a particular term or "interpret" a computed value. Make sure that you review the definitions. To aid your preparation make sure that you can do the following:

  • State the General Linear Model.
    Note: Remember that you must state the expression and the axioms.
  • Given SAS output for the REG procedure, provide estimates for the parameters of a multiple regression model.
    Note: Remember that the standard deviation about the regression surface is a parameter.
  • Given SAS output for the REG procedure, comment on model adequacy.
    Note: That is, formulate hypotheses and discuss the corresponding p-values. Also, interpret R².
  • Briefly discuss the process used to obtain Principal Components and state what a principal component is, in terms of the original variables.

  These terms are defined in the lecture notes and/or the handouts. Practice problems and solutions for computational problems (e.g. determinants, eigenvalues, etc.) are available. Here are some more practice problems.