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 \(y_i = \beta_0 + \beta_1x_i + \epsilon_i\).

Textbook

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Data sets

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