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  2. "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
  3. <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"><head>
  4. <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
  5. <meta name="Author" lang="en" content="Miguel Casquilho" />
  6. <title>M&middot;C, IST: simple linear regression</title>
  7. <link rel="stylesheet" type="text/css"
  8. href="http://web.tecnico.ulisboa.pt/~mcasquilho/commonstyle.css" />
  9. </head> <!-- 18-Aug-2008 -->
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  11. <form method="post" action=
  12. "http://web.tecnico.ulisboa.pt/~mcasquilho/cgi-bin/interfacepng.php?regrsimplin">
  13. <input name="executable" type="hidden" value="regrsimplin.exe" />
  15. <table width="90%" bgcolor="#eeeeee" align="center" border="1" class="sm">
  16. <tr><td colspan="3">
  17. <table width="100%" class="sm">
  18. <tr><td width="50px"><a href='https://fenix.ist.utl.pt/departamentos/deq'><img alt='&copy;'
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  20. width='40' height='41' /></a>
  21. </td><!-- title -->
  22. <td><div style="font-size: 13.5pt; text-align: center"><!-- title --><b
  23. onmouseout="this.style.color='blue', this.style.fontStyle='normal'"
  24. onmouseover="this.style.color='red',
  25. this.style.fontStyle='bold'">
  26. Simple
  27. linear regression</b></div>&emsp;
  28. Performs a simple linear regression analysis on user-supplied data.
  29. <!-- b>Under construction</b --></td>
  30. <td width="112px"><table width='100%'>
  31. <tr><td align='center' bgcolor='white'>
  32. <input type="submit"
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  34. onmouseout="this.style.fontStyle='normal', this.style.fontWeight='normal'"
  35. onmouseover="this.style.fontStyle='normal', this.style.fontWeight='bold'" /></td>
  36. </tr><tr><td align='center'><span style='font-size:
  37. xx-small'>2021.Mar.16 03:50:06</span></td></tr>
  38. </table>
  39. </td></tr></table>
  40. </td></tr> <!-- ................................................... -->
  42. <tr><td width="15%" align="center"><i>n</i></td>
  43. <td width="45%"><input name="n" type="text" value="10" size="5"
  44. maxlength="3" /></td>
  45. <td width="40%"><i>Number</i> of data. &bull;</td></tr>
  47. <tr><td align="center"><i>X</i> data</td>
  48. <td colspan="2"><i>Independent</i> variable, <i>X</i> &bull;<br />
  49. <textarea name="x" style="color: blue; font-weight: bold" cols="63" rows=
  50. "1"> .000 .204 .306 .408 .510 .612 .714 .816 .918 1.02</textarea></td>
  51. </tr>
  53. <tr><td align="center"><i>Y</i> data</td>
  54. <td colspan="2"><i>Dependent</i> variable, <i>Y</i> &bull;<br />
  55. <textarea name="y" style="color: blue; font-weight: bold" cols="63" rows=
  56. "1"> .00 .04 .06 .08 .11 .13 .15 .18 .20 .23</textarea></td>
  57. </tr>
  59. <tr><td align="center">Switch <i>X</i> and <i>Y</i> ?</td>
  60. <td><select name="iswitch"><option value="0" selected="selected">No</option>
  61. <option value="1">Yes</option></select> &nbsp;
  62. (<i>No:</i> as above; <i>Yes:</i> opposite)</td>
  63. <td><i>Switch</i> the values above (indep. and dep. vars.).</td></tr>
  65. <tr><td align="center">Through origin ?</td>
  66. <td><input type="radio" name="ithruorig" value="0" checked="checked" />No
  67. <input type="radio" name="ithruorig" value="1" />Yes</td>
  68. <td>Constrain line to pass <i>through the origin</i>. &bull;</td></tr>
  70. <tr><td align="center"><i>x</i><sub>T</sub>,
  71. <i>y</i><sub>T</sub></td>
  72. <td><input name="xt" type="text" value="0" size="5"
  73. maxlength="5" /><input name="yt" type="text" value="0" size="5"
  74. maxlength="5" /></td>
  75. <td>Trial <i>x</i> and <i>y</i> for estimation. &bull;</td></tr>
  77. <tr><td align="center">Show values</td>
  78. <td><select name="ishow"><option value="0" selected="selected">No</option>
  79. <option value="1">Yes</option></select></td>
  80. <td>Shows the coordinates of the graph. &bull;</td></tr>
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  89. 22 dark gray 404040, 23 olive green 408000, 24 navy blue 000080, 25 806010,
  90. 26 806060, 27 ~806080, 28 ~5050c0, 29 0000ff, 30 006000, 31 ~eb0c0,
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  92. <!-- plot gnudata.dat \ (or anything: this line is a MANDATORY dummy) -->
  94. <tr><td colspan="3"><input name="gnuplot" type="hidden"
  95. value="set terminal png enhanced font 'FreeSerif, 13' size 500, 380
  96. set timestamp font 'FreeSerif, 10' offset 5, -0.7
  97. set nokey; set title 'Simple linear regression' offset 0, +.5
  98. set xlabel 'x' offset 12, .1; set ylabel 'y'
  99. plot 'anyname.dat' \
  100. using 1:2 with linespoints linetype 1 linewidth 2 ps 2 pt 12, \
  101. '' using 1:3 with lines linetype 2 linewidth 3, \
  102. '' using 1:4 with lines linetype 3 linewidth 2, \
  103. '' using 1:5 with lines linetype 3 linewidth 2" />
  104. <table width="100%" class="sm">
  105. <tr><td valign="top" colspan="2">&emsp;From a given set of <i>data</i>
  106. (points, observations), calculates the straight line,&emsp;
  107. <i>y</i> = <i>a</i><sub>0</sub> + <i>a</i><sub>1</sub> <i>x</i>,
  108. &nbsp;that best fits the data.
  109. <br />&emsp;If "switch", the <i>X</i> and <i>Y</i>
  110. are switched just <i style="color: red">after</i> being printed.
  111. <br />&emsp;For <i>x</i><sub>T</sub> and <i>y</i><sub>T</sub>,
  112. the estimated <i>y</i>&circ;<sub>T</sub> and <i>x</i>&circ;<sub>T</sub>,
  113. respectively, are calculated, with their confidence intervals.
  114. <br />&emsp;[The Pr above <i>F</i> (its p-value) tests
  115. a <i>null slope</i> (no influence): Pr(<i>a</i><sub>1</sub> &ne; 0).
  116. I.e., if small p-value, <i>a</i><sub>1</sub> &ne; 0.]
  117. <br />&emsp;Other suggested data:
  118. <table class="sm">
  119. <tr valign="top"><td><i>n</i> = 10 &nbsp; </td>
  120. <td><i>X</i> =&emsp; 75 80 93 65 87 71 98 68 84 77
  121. <br /><i>Y</i> =&emsp; 82 78 86 72 91 80 95 72 89 74</td>
  122. <td>&rarr; <i>a</i><sub>0, 1</sub> = 29.13, 0.661;
  123. <br />&nbsp; (switch) &minus;14.39, 1.15</td><td>[Spiegel, 1975, 300,
  124. <br />Pr. 8.67]</td></tr>
  125. <tr valign="top"><td><i>n</i> = 20 &nbsp; </td>
  126. <td><i>X</i> =&nbsp; 5.5 4.8 4.7 3.9 4.5 6.2 6.0 5.2 4.7 4.3 4.9 5.4 5.0 6.3
  127. 4.6 4.3 5.0 5.9 4.1 4.7
  128. <br /><i>Y</i> =&nbsp; 3.1 2.3 3.0 1.9 2.5 3.7 3.4 2.6 2.8 1.6 2.0 2.9 2.3 3.2
  129. 1.8 1.4 2.0 3.8 2.2 1.5</td>
  130. <td>&rarr; <i>a</i><sub>0, 1</sub> = &minus;1.700, 0.840</td>
  131. <td>[Marshall, 2005, 5]</td></tr>
  132. </table></td></tr>
  133. </table></td></tr>
  135. <tr><td align="center"><input type="reset"
  136. style="font-size: smaller" value=" Reset " /></td><td><i>References:</i></td>
  137. <td align="center">Plate: SimpLinReg08819</td></tr>
  138. <tr><td colspan="3"><p class="ref">&bull;&nbsp;<a href=
  139. "http://people.clemson.edu/~jerryh/"><span class="sc">Hester</span></a>,
  140. Jerry D.: <a href=
  141. "http://phoenix.phys.clemson.edu/tutorials/excel/regression.html">Linear
  142. Regression &amp; Excel</a> (<a href=
  143. "http://phoenix.phys.clemson.edu/tutorials/excel/">Excel Tutorials</a>),
  144. <a href="http://www.clemson.edu/">Clemson Univ.</a>.</p>
  146. <p class="ref">&bull;&nbsp;<a href=
  147. "http://www.si.umich.edu/Classes/644/"><span class="sc">Resnick</span></a>,
  148. Paul: <a href="./,regression/Resnick.ch11.pps">Chap. 11</a>.<i>pps</i>
  149. [McClave &amp; Sincich, 2003?] (SI 644--Introductory Statistics
  150. &amp; Data Analysis,
  151. <a href="http://www.si.umich.edu/">Univ. of Michigan</a>).</p>
  153. <p class="ref">&bull;&nbsp;<a href=
  154. "http://www.math.tulane.edu/~mlacey/"><span class="sc">Lacey</span></a>,
  155. Michelle: <a href=
  156. "http://www.stat.yale.edu/Courses/1997-98/101/anovareg.htm">ANOVA for
  157. regression</a> (Dept. Stat., Yale Univ.), <a href=
  158. "http://www.math.tulane.edu/">Tulane Univ.</a>.</p>
  160. <p class="ref">&bull;&nbsp;<a href=
  161. "http://www.che.udel.edu/directory/facultyprofile.html?id=399"><span
  162. class="sc">Shine</span></a>, Annette D.: <a href=
  163. "http://www.che.udel.edu/pdf/FittingData.pdf">Fitting data</a>.<i>pdf</i>
  164. (<a class="decnone" href="./,regression/UDel.FittingData.pdf">=</a>),
  165. <a href="http://www.udel.edu/">Univ. Delaware</a>
  166. (S. I. <a href="http://www.che.udel.edu/directory/facultyprofile.html?id=
  167. 375">Sandler</a>).</p>
  169. <p class="ref">&bull;&nbsp;<a href=
  170. "http://evergreen.loyola.edu/chm/www/"><span class="sc">Morrell</span></a>,
  171. Christopher H.: <a href=
  172. "http://evergreen.loyola.edu/chm/www/st466/teachingstat-rto.pdf">Regression
  173. through the origin</a>.<i>pdf</i> (accessed 2008-08-19)
  174. (<a class="decnone" href="http://web.tecnico.ulisboa.pt/~mcasquilho/compute/errtheory/,regression/regrthroughorigin.pdf">=</a>),
  175. <a href="http://www.loyola.edu/">Loyola Coll.</a>.</p>
  177. <p class="ref">&bull;&nbsp;<span class="sc">Weisstein</span>, Eric W.,
  178. "<a href="http://mathworld.wolfram.com/LeastSquaresFitting.html">Least
  179. squares fitting</a>". From <i>MathWorld</i> &mdash; a Wolfram Web Resource
  180. (accessed 2008-08-19).</p>
  182. <p class="ref">&bull;&nbsp;<span class="sc">Taylor</span>, John R.,
  183. <acronym title="BibIST"><a href=
  184. "http://thesaurus.reitoria.utl.pt/search~S3*por?/cQC39.TAY.67208/
  185. cqc+++39+tay67208/-3,-1,0,B/
  186. frameset&amp;FF=cqc+++39+tay67208&amp;1,1,">1997</a></acronym>,
  187. "An introduction to error analysis", 2.nd ed., <acronym title="Amazon"><a href=
  188. "http://www.amazon.co.uk/In
  189. troduction-Error-Analysis-Uncertainties-Measurements/
  190. dp/093570275X/ref=sr_1_1?ie=UTF8&amp;s=books&amp;qid=1217804330&amp;sr=1-1"
  191. >Univ. Sci. Books</a></acronym>
  192. (<a href="http://www.uscibooks.com">USB</a>), Sausalito, CA (USA)
  193. (<a href="http://physics.gac.edu/~mellema/Taylor/
  194. Taylor_files/frame.htm">intro</a> IE).</p>
  196. <p class="ref">&bull;&nbsp;<span class="sc">McClave</span>, James T. and
  197. Terry <span class="sc">Sincich</span>,
  198. <acronym title="Amazon"><a href=
  199. "http://www.amazon.co.uk/Statistics-James-T-McClave/dp/0132363445/ref=
  200. sr_1_9?ie=UTF8&amp;s=books&amp;qid=1221003962&amp;sr=1-9"> 2003</a>?</acronym>,
  201. "Statistics", 9.th ed. (now 11.th), Pearson Intn'l Ed. (Pr.-Hall).</p>
  203. <p class="ref">&bull;&nbsp;<span class="sc">Spiegel</span>, Murray R.,
  204. 1975, Schaum's Outline Series, "Theory and problems of Probability and
  205. Statistics", McGraw-Hill Book Co., New York, NY (USA), ISBN 0-07-060220-4;
  206. <acronym title="BibIST"><a href=
  207. "http://thesaurus.reitoria.utl.pt/search~S3*por?/aSpiegel/aspiegel/1,8,40,B/
  208. frameset&amp;FF=aspiegel+murray+r&amp;19,,24">1980</a></acronym>,
  209. ISBN 0-07-084356-2;
  210. <acronym title="Amazon"><a href=
  211. "http://www.amazon.co.uk/Schaums-Outline-Probability-Statistics/dp/
  212. 0071350047/ref=sr_1_1?ie=UTF8&amp;s=books&amp;qid=
  213. 1220739410&amp;sr=1-1">2000</a></acronym>, ISBN 0-07-135004-7.</p>
  215. <p class="ref">&bull;&nbsp;<a href=
  216. "http://filebox.vt.edu/users/jemarsh2/"><span class="sc">Marshall</span></a>,
  217. J. Brooke: <a href="./,regression/VirgTech_Ch10Examples.pdf">Simple
  218. Linear Regression</a>.<i>pdf</i> Examples (Virginia Tech).</p>
  220. <p class="ref">&bull;&nbsp;1584-08-19: <a href=
  221. "http://www-groups.dcs.st-and.ac.uk/~history/Biographies/
  222. Vernier.html">Vernier</a>, Pierre, birthday. [Compare with <a href=
  223. "http://www-groups.dcs.st-and.ac.uk/~history/Biographies/
  224. Clavius.html">Clavius</a> (1538&ndash;1612) and Pedro <a href=
  225. "http://www-groups.dcs.st-and.ac.uk/~history/Biographies/
  226. Nunes.html">Nunes</a> (1502&ndash;1578) about the <a href=
  227. "http://www.merriam-webster.com/dictionary/vernier"><i>vernier</i></a> or
  228. &mdash;generally absent from the dictionaries&mdash; <a href=
  229. "http://www.websters-online-dictionary.org/definition/
  230. nonius"><i>nonius</i></a>.]</p>
  231. </td></tr>
  232. </table>
  233. </form>
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  247. <td width="70%" align=
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  249. <i>Created:</i> 2008-08-19 &mdash; <i>Last modified:</i>
  250. 2008-09-15</td></tr></table>
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