Regression Examples - Revision history

Rb: /* Exercises */

2013-10-04T16:45:34Z

‎Exercises

Rb: /* Exercises */

2013-10-04T16:16:43Z

‎Exercises

Rb: /* Exercises */

2013-09-25T21:24:00Z

‎Exercises

Rb: /* Exercises */

2013-09-25T21:22:59Z

‎Exercises

Rb: /* Exercises */

2013-09-25T21:02:56Z

‎Exercises

Rb: /* Exercises */

2013-09-25T21:00:09Z

‎Exercises

Rb: /* Exercises */

2013-09-25T20:12:11Z

‎Exercises

Admin: /* Exercise 1 */

2013-08-05T21:00:37Z

‎Exercise 1

Admin: /* Exercise 1 */

2013-08-05T20:57:34Z

‎Exercise 1

Admin at 20:56, 5 August 2013

2013-08-05T20:56:28Z

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 = Exercises =
-Solutions in curly {curly brackets}. Worked solution clips can be found here [http://youtu.be/Nq3Z7bqoUYM?hd=1 Q1], [http://youtu.be/zIIidXiLhPE?hd=1 Q2], [http://youtu.be/GVOO3jvSNNs?hd=1 Q3] and [].
+Solutions in curly {curly brackets}. Worked solution clips can be found here [http://youtu.be/Nq3Z7bqoUYM?hd=1 Q1], [http://youtu.be/zIIidXiLhPE?hd=1 Q2], [http://youtu.be/GVOO3jvSNNs?hd=1 Q3] and [http://youtu.be/d4YLj2fUbSI?hd=1 Q4].
 <ol>
 <li><p>Within an area of <math>4</math> square miles, in a city centre, there are <math>10</math> petrol stations. The following table gives the price charged at each petrol station (in pence per litre) for unleaded petrol, and the market share obtained:</p>

@@ Line 4: / Line 4: @@
 = Exercises =
-Solutions in curly {curly brackets}. Worked solution clips can be found here [http://youtu.be/Nq3Z7bqoUYM?hd=1 Q1], [http://youtu.be/zIIidXiLhPE?hd=1 Q2], [] and [].
+Solutions in curly {curly brackets}. Worked solution clips can be found here [http://youtu.be/Nq3Z7bqoUYM?hd=1 Q1], [http://youtu.be/zIIidXiLhPE?hd=1 Q2], [http://youtu.be/GVOO3jvSNNs?hd=1 Q3] and [].
 <ol>
 <li><p>Within an area of <math>4</math> square miles, in a city centre, there are <math>10</math> petrol stations. The following table gives the price charged at each petrol station (in pence per litre) for unleaded petrol, and the market share obtained:</p>

@@ Line 4: / Line 4: @@
 = Exercises =
-Solutions in curly {curly brackets}. Worked solution clips can be found here [http://youtu.be/Nq3Z7bqoUYM Q1], [http://youtu.be/zIIidXiLhPE Q2], [] and [].
+Solutions in curly {curly brackets}. Worked solution clips can be found here [http://youtu.be/Nq3Z7bqoUYM?hd=1 Q1], [http://youtu.be/zIIidXiLhPE?hd=1 Q2], [] and [].
 <ol>
 <li><p>Within an area of <math>4</math> square miles, in a city centre, there are <math>10</math> petrol stations. The following table gives the price charged at each petrol station (in pence per litre) for unleaded petrol, and the market share obtained:</p>

@@ Line 4: / Line 4: @@
 = Exercises =
-Solutions in curly {curly brackets}. Worked solution clips can be found here [http://youtu.be/Nq3Z7bqoUYM Q1], [], [] and [].
+Solutions in curly {curly brackets}. Worked solution clips can be found here [http://youtu.be/Nq3Z7bqoUYM Q1], [http://youtu.be/zIIidXiLhPE Q2], [] and [].
 <ol>
 <li><p>Within an area of <math>4</math> square miles, in a city centre, there are <math>10</math> petrol stations. The following table gives the price charged at each petrol station (in pence per litre) for unleaded petrol, and the market share obtained:</p>

@@ Line 4: / Line 4: @@
 = Exercises =
-Solutions in curly {curly brackets}.
+Solutions in curly {curly brackets}. Worked solution clips can be found here [http://youtu.be/Nq3Z7bqoUYM Q1], [], [] and [].
 <ol>
 <li><p>Within an area of <math>4</math> square miles, in a city centre, there are <math>10</math> petrol stations. The following table gives the price charged at each petrol station (in pence per litre) for unleaded petrol, and the market share obtained:</p>

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 <li><p>Show that the correlation coefficient between these two variables is -0.8366. Interpret this number and, in particular, is the sign as you would expect?</p></li>
 <li><p>Use the data to fit the regression line, <math>\hat{y}=a+bx</math>; i.e., show that regressing <math>y</math> on <math>x</math> yields a value of <math>a=2.4241</math> and <math>b=-0.0172</math>. Why would you expect the value of <math>b</math> to be negative given (a)?</p></li>
-<li><p>Suppose that every price rises uniformly by <math>2</math> pence. Assuming that the market shares stay the same, write down what a regression of ''market share''on ''prices'' would now yield for values of <math>a</math> and <math>b</math>. Think, rather than calculate.</p></li></ol>
+<li><p>Suppose that every price rises uniformly by <math>2</math> pence. Assuming that the market shares stay the same, write down what a regression of ''market share''on ''prices'' would now yield for values of <math>a</math> and <math>b</math>. Think, rather than calculate. {2.4586}</p></li></ol>
 </li>
 <li><p>Refer to the data given below in which you are given <math>11</math> observations on a variable labeled <math>X</math> and <math>11</math> observations on each of three variables <math>Y</math>, <math>Z</math> and <math>W</math>.</p>

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 = Exercises =
+Solutions in curly {curly brackets}.
 <ol>
 <li><p>Within an area of <math>4</math> square miles, in a city centre, there are <math>10</math> petrol stations. The following table gives the price charged at each petrol station (in pence per litre) for unleaded petrol, and the market share obtained:</p>
@@ Line 54: / Line 54: @@
 <ol>
-<li><p>Calculate the sample (or arithmetic) mean and the sample standard deviation of the price.</p></li>
+<li><p>Calculate the sample (or arithmetic) mean and the sample standard deviation of the price. {138.4,3.765}</p></li>
-<li><p>Calculate the ''weighted'' mean, using the market share values as the set of weights. Explain why the weighted and unweighted means differ.</p></li>
+<li><p>Calculate the ''weighted'' mean, using the market share values as the set of weights. Explain why the weighted and unweighted means differ. {132.6}</p></li>
-<li><p>Calculate the (sample) mean and standard deviation of the price per gallon.</p></li></ol>
+<li><p>Calculate the (sample) mean and standard deviation of the price per gallon. {626.166; 17.1157}</p></li></ol>
 </li>
 <li><p>Consider, again, the data on <math>X=</math> ''petrol prices'' and <math>Y=</math> ''market share'' given in the previous question. You must find the answers to the following questions &quot;by hand&quot; so that you understand the calculations involved; however, you should also check you answers using EXCEL, MATLAB or any other software package.</p>

← Older revision		Revision as of 21:00, 5 August 2013
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−	= ~~Exercise 1~~ =	+	= Exercises =

	<ol>		<ol>

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 <li><p>To what extent do you feel that ''correlation'' and ''regression'' analysis is useful for the various pairs of variables?</p></li></ol>
 </li>
-<li><p>In this file [[media:GDP<sub>C</sub>O2.xlsx|GDP<sub>C</sub>O2.xlsx]] you can find data for carbon dioxide (CO2) emissions and the Gross Domestic Product (GDP) for 39 European countries for the year 2009.</p>
+<li><p>In this file [[media:GDP_CO2.xlsx|GDP_CO2.xlsx]] you can find data for carbon dioxide (CO2) emissions and the Gross Domestic Product (GDP) for 39 European countries for the year 2009.</p>
 <ol>
 <li><p>Using EXCEL, construct a scatter plot of carbon dioxide emissions against gross domestic product, construct the regression line (of CO2 on GDP) and calculate the correlation coefficient.</p></li>

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 = Exercise 1 =
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 <li><p>Within an area of <math>4</math> square miles, in a city centre, there are <math>10</math> petrol stations. The following table gives the price charged at each petrol station (in pence per litre) for unleaded petrol, and the market share obtained:</p>
 <table border="1">
-<thead>
 <tr class="header">
 <th align="center">Petrol Station</th>
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 <th align="center"><math>10</math></th>
 </tr>
-</thead>
 <tr class="odd">
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 <li><p>Refer to the data given below in which you are given <math>11</math> observations on a variable labeled <math>X</math> and <math>11</math> observations on each of three variables <math>Y</math>, <math>Z</math> and <math>W</math>.</p>
 <table border="1">
-<thead>
 <tr class="header">
 <th align="center">observation</th>
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 <th align="right"><math>\quad w</math></th>
 </tr>
-</thead>
 <tr class="odd">