Q2. Consider an experiment to compare six oil refineries. Three refineries are in Texas and three are in Oklahoma The observed variable is the amount of gasoline produced in a day. For each refinery, there are obscrvations on two days. We write a model for these data as Yjk =H+a; + Bij +ejk; i=1, 2;j=1,2, 3; k=1, 2. Here a refers to the state, and B refers to the refinery within state. This model can be written as a lincar model Y = XBß+e, where, B = (µ, a,, az, B11, Bı2, B13, B21, B22, B23)'. (a) Write out Y, X, and e for this model. (b) Compute XX. (c) Show that X is not of full column rank. Specifically, show that there are three columns of X that can be written as linear combinations of the other six columns. (d) Show that the remaining six columns of X are linearly independent. ге

Q2. Consider an experiment to compare six oil refineries. Three refineries are in Texas and three are in Oklahoma The observed variable is the amount of gasoline produced in a day. For each refinery, there are obscrvations on two days. We write a model for these data as Yjk =H+a; + Bij +ejk; i=1, 2;j=1,2, 3; k=1, 2. Here a refers to the state, and B refers to the refinery within state. This model can be written as a lincar model Y = XBß+e, where, B = (µ, a,, az, B11, Bı2, B13, B21, B22, B23)'. (a) Write out Y, X, and e for this model. (b) Compute XX. (c) Show that X is not of full column rank. Specifically, show that there are three columns of X that can be written as linear combinations of the other six columns. (d) Show that the remaining six columns of X are linearly independent. ге

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 2EQ: 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed...

See similar textbooks