Homework 1: Due Tuesday, September 6th

  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 Thursday, September 15th

Note: In order to receive full credit, please explain your answers well. Simple yes/no answers will not be given credit.

  1. 1.19 (For part b., use \(R\))
  2. 1.20 (For part b., use \(R\))
  3. 1.23
  4. 1.24

Homework 3: Due Thursday, September 22nd

You are turning in two files. 1. Hand written work. 2. A 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 fine but using R would be easier. I will accept the answer either way)
  6. 5.12 (Hand calculations are fine but using R would be easier. I will accept the answer either way)
  7. 5.14 (Hand calculations are fine but using R would be easier. I will accept the answer either way)

Homework 4: Due Thursday, September 29th

Turn in your homework only as a 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 matrix methods, obtain the vector of estimated regression coefficients and vector of residuals.
  2. Find the hat matrix \(\bf{H}\).
  3. Find \(s^2(e)\).
  1. Refer to $ Problems 1.22 and 5.7. Using matrix methods, obtain the following:
  1. \((X' X)^{-1}\)
  2. \(\bf{b}\)
  3. \(\bf{\hat{Y}}\)
  4. \(\bf{e}\)
  5. \(\bf{H}\)

Homework 5: Due Thursday, October 12th

Turn in your homework only as a 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

Homework 6: Due Thursday, October 19th

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

  1. 6.5 (except part f)
  2. 6.15
  3. 6.7
  4. 6.8
  5. 6.16
  6. 6.17

Homework 7: Due Thursday, October 26th

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

  1. 9.10
  2. 9.11
  3. 9.18 (Ignore the second half of the part a))
  4. 9.22

Homework 8: Due Thursday, December 6th

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

  1. 14.7
  2. 14.11
  3. 14.18
  4. 14.20
  5. 14.22

Textbook

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Data sets

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