Homework 1: Due Tuesday, September 2nd

  1. (1.2)

  2. (1.5 Give reason for your answer)

  3. (1.12)

  4. A regression model is \(y = \beta_0 + \beta_1x + \epsilon\). There are six observations. The summary statistics are:

\[\sum y_i = 8.5,\quad \sum x_i = 6,\quad \sum x_i^2 = 16,\quad \sum x_iy_i = 15.5,\quad \sum y_i^2 = 17.25\] Calculate the LS estimate of \(\beta_1\)

  1. You are fitting a linear regression model \(y_i = \beta_0 + \beta_1x_i + \epsilon_i\) to 18 observations. You are given the followings:

\[\sum y_i = 252,\quad \sum x_i = 216,\quad \sum x_i^2 = 3092,\quad \sum x_iy_i = 3364,\quad \sum y_i^2 = 4528\] Calculate the LS estimate of \(\beta_1\)

  1. You are fitting a linear regression model \(y_i = \beta_0 + \beta_1x_i + \epsilon_i\) to the following data:
x 2 5 8 11 13 15 16 18
y -10 -9 -4 0 4 5 6 8

Calculate the LS estimate of \(\beta_1\) using \(R\)

  1. Given the following information

\[\sum y_i = 1742,\quad \sum x_i = 144,\quad \sum x_i^2 = 2300,\quad \sum x_iy_i = 26696,\quad \sum y_i^2 = 312674 \quad n = 12\] Determine the LS equation for the model \(y_i = \beta_0 + \beta_1x_i + \epsilon_i\).

Homework 2: Due Tuesday, September 9th

To receive full credit, please provide detailed explanations for your answers. Simple “yes” or “no” responses will not be accepted. Submit your homework as a printed PDF or handwritten work—do not email it in whole or in part. Homework is due in class.

  1. 1.19 (use \(R\) as needed)
  2. 1.20 (use \(R\) as needed)
  3. 1.23 (use \(R\) as needed)
  4. 1.24 (use \(R\) as needed)

Homework 3: Due Tuesday, September 16th

You are turning in two files. 1. Hand written work. 2. A printed pdf created by Rmarkdown for the problems where it says “Use R to check your answers”.

  1. 5.1 (Show work by hand calculations. Use R to check your answers)
  2. 5.3 (Hand calculations only)
  3. 5.4 (Show work by hand calculations. Use R to check your answers)
  4. 5.6 (Show work by hand calculations. Use R to check your answers)
  5. 5.10 (Hand calculations are encouraged but using R would be easier. I will accept the answer either way)
  6. 5.12 (Hand calculations are encouraged but using R would be easier. I will accept the answer either way)
  7. 5.14 (Hand calculations are encouraged but using R would be easier. I will accept the answer either way)

Homework 4: Due Thursday, September 25th

Turn in your homework only as a printed pdf created in \(R\). No handwritten work please!

  1. Refer to \(\textbf{consumer finance}\) problems 5.5 and 5.13 in the text book.
    1. Using the matrix method, obtain the vector of estimated regression coefficients and vector of residuals.
    2. Find the hat matrix \(\bf{H}\).
    3. Find \(s^2(e)\).
  2. Refer to \(\textbf{Plastic hardness}\) Problems 1.22 and 5.7. Using matrix methods, obtain the following:
    1. \((\bf{X' X})^{-1}\)
    2. \(\bf{b}\)
    3. \(\bf{\hat{Y}}\)
    4. \(\bf{e}\)
    5. \(\bf{H}\)

Homework 5: Due Thursday, October 2nd

Turn in your homework only as a printed pdf created in \(R\). No handwritten work please!

  1. 3.3 - Note: for part e) conduct the Breusch-Pagan test instead Brown-Forsythe test using \(\alpha = 0.01\)
  2. 3.4
  3. 3.11
  4. 3.15
  5. 3.17

Textbook

Download PFD textbook here

Data sets

Click here to get Data sets to use in the assignments