Homework 1: Due Tuesday, September
2nd
- (1.2) 
- (1.5 Give reason for your answer) 
- (1.12) 
- 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 \(\beta_1\)
- 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 \(\beta_1\)
- You are fitting a linear regression model \(y_i = \beta_0 + \beta_1x_i + \epsilon_i\)
to the following data:
Calculate the LS estimate of \(\beta_1\) using \(R\)
- 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.
- 1.19 (use \(R\) as needed)
- 1.20 (use \(R\) as needed)
- 1.23 (use \(R\) as needed)
- 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”.
- 5.1 (Show work by hand calculations. Use R to check your
answers)
- 5.3 (Hand calculations only)
- 5.4 (Show work by hand calculations. Use R to check your
answers)
- 5.6 (Show work by hand calculations. Use R to check your
answers)
- 5.10 (Hand calculations are encouraged but using R would be
easier. I will accept the answer either way)
- 5.12 (Hand calculations are encouraged but using R would be
easier. I will accept the answer either way)
- 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!
- Refer to \(\textbf{consumer
finance}\) problems 5.5 and 5.13 in the text book.
- Using the matrix method, obtain the vector of estimated regression
coefficients and vector of residuals.
- Find the hat matrix \(\bf{H}\).
- Find \(s^2(e)\).
 
- Refer to \(\textbf{Plastic
hardness}\) Problems 1.22 and 5.7. Using matrix methods, obtain
the following:
- \((\bf{X' X})^{-1}\)
- \(\bf{b}\)
- \(\bf{\hat{Y}}\)
- \(\bf{e}\)
- \(\bf{H}\)
 
 
Homework 5: Due Thursday, October 2nd
Moved to Tuesday October 7th
Turn in your homework only as a printed pdf created in \(R\). No handwritten work please!
- 3.3 - Note: for part e) conduct the Breusch-Pagan test instead
Brown-Forsythe test using \(\alpha =
0.01\)
- 3.4
- 3.11
- 3.15
5) 3.17 Moved to next HW
 
Homework 6: Due Tuesday, October 20th
Turn in your homework only as a printed pdf created in \(R\). No handwritten work please!
- 3.6 a), b), c) Only
- 3.16
- 3.17
 
Homework 7: Due Thursday, October
30th
Turn in your homework only as a pdf created in \(R\). No handwritten work please!
- 6.5 (except part f)
- 6.7
- 6.8
 
Data sets
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here to get Data sets to use in the assignments