.MCAD 308000000 \  docDocumentMmcObject[ÿÿÿÿ++ d2_graph_format graphData% axisFormat)L)Ltrace2D&&&&&&&&& & & & & &&& dim_formatTmasslengthtimecharge temperature luminosity substancecriptionNumericalFormatQdii shpRectVmcDocumentObjectState\ð´ mcPageModelKš™™?XU™?š™™?š™™?mcHeaderFooterI |F@I|Dpage |P CHeaderFooterJA{\rtf1\ansi\ansicpg1252\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq14 Arial;}{\f3\fswiss\fprq15 Arial;}{\f4\fnil\fprq15 Arial;}} {\colortbl\red0\green0\blue0;} \deflang1033\pard\plain\f3\fs18 \par } A {\rtf1\ansi\ansicpg1252\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq14 Arial;}{\f3\fswiss\fprq15 Arial;}{\f4\fnil\fprq15 Arial;}} {\colortbl\red0\green0\blue0;} \deflang1033\pard\qc\plain\f2\fs20 \{f\} \par } A{\rtf1\ansi\ansicpg1252\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq14 Arial;}{\f3\fswiss\fprq15 Arial;}{\f4\fnil\fprq15 Arial;}} {\colortbl\red0\green0\blue0;} \deflang1033\pard\qr\plain\f3\fs18 \par } @J{d}page {n}@J@Jü©ñÒMbP?ü©ñÒMbP? TextState? TextStyle>@ ArialSerial_ParPropDefaultW?Normalÿÿÿÿÿÿÿÿ€font_style_listO font_stylePóÿÿÿöÿÿÿ ÿÿÿÿ VariablesArial@Póÿÿÿöÿÿÿ ÿÿÿÿ ConstantsTimes New Roman@Póÿÿÿöÿÿÿ ÿÿÿÿTextArial@Póÿÿÿöÿÿÿ ÿÿÿÿGreek VariablesSymbol@Póÿÿÿöÿÿÿ ÿÿÿÿUser^1Arial@Póÿÿÿöÿÿÿ ÿÿÿÿUser^2 Courier New@Póÿÿÿóÿÿÿ ÿÿÿÿUser^3System@Póÿÿÿöÿÿÿ ÿÿÿÿÿUser^4Script@Póÿÿÿöÿÿÿ ÿÿÿÿÿUser^5Roman@Póÿÿÿöÿÿÿ ÿÿÿÿÿUser^6Modern@Póÿÿÿöÿÿÿ ÿÿÿÿUser^7Times New Roman@Póÿÿÿöÿÿÿ ÿÿÿÿSymbolsSymbol@Póÿÿÿóÿÿÿ ÿÿÿÿCurrent Selection FontArial@Póÿÿÿóÿÿÿ ÿÿÿÿUndefined Font@Póÿÿÿóÿÿÿ ÀÀÀHeaderArial@Póÿÿÿóÿÿÿ ÀÀÀFooterArial@Póÿÿÿöÿÿÿ ÿÿÿÿRotated Math FontArial9 TextRegion* docRegionGshpBoxU % +•èè CharacterMap-RangeMap;/Linear Least Squares Fitting: Mathcad Template  ChrPropMap7../ RangeElem<.  ChrPropData8 RangeData=lArial0,0,128 < 8nArial0,0,128  ParPropMap9/ </5?<5@@0ÿÿÿÿ@NormalArialÿÿÿ @A@B@U2FD!@•@B@@ p@C@@ŒÁ€@B@D@@d@CN@E@@–Ä€@C@F@@+@@ESerial_DisplayNodeX@G@@¤@E _n_u_l_l_@H*@US/“`§2@@-@¹The first column of the matrix DATA (containing the x values) is set equal to an array x. Similarly, an array containing the y values is defined from the second column of matrix DATA.7¹900‰¹@I<0@J:@Wÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ@K<‰@L:@W?@I@K@K1@M</¹@N<¹@O0ÿÿÿÿ@NormalArialÿÿÿ @P@B@UVhl h’@Q@@ p@R@@ Á€@Q@S@@d@Rx@T@@4ý€@R@U@@d@TDATA@V@@´@T0@W@B@UvhŒ ˆ“@X@@ p@Y@@ Á€@X@Z@@d@Yy@[@@4ý€@Y@\@@d@[DATA@]@@´@[1@^*@U«"K¸      -CNOTE: This mathcad document can be used as a template for all the linear-least squares fitting assignments that you will encounter. When ask to obtain a 'best-fit' line for an x-y data set, carry out the following steps: either type your data directly into the x and y arrays shown above or (1) use a text editor (such as Microsoft Word) to creat a file that holds the x-values in column one and the y-values in column two, (2) save the data as a text file, giving the file an appropriate filename and placing the file in the same folder as this mathcad document, and (3) open this mathcad document and edit the above statement DATA := READPRN("sampledata.txt") so that it contains the proper filename that you created in step 2. No other changes will need to be made to this document.7Ì@_<@`8@^gArial0,0,128@a<¿@b8@^0,0,128@_@c< @d8@^kArial0,0,128@a@eThis expression evaluates the y-intercept of the best-fit line7>9>@Û<>@Ü:@Wÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ1@Ý</>@Þ<>@ß0ÿÿÿÿ@NormalArialÿÿÿ @à@B@U´ è¿@á@@ p@â@@ Á€@á@ã@@d@âb@ä@@û€@â@å@@ˆÇ@@ä@æ@@Ê@@å@ç@@Žp@@æ@è@@É€@ç@é@@d@èi@ê@@ý€@è@ë@@d@êy@ì@@¤@êi@í@@Žp€@æ@î@@É€@í@ï@@d@îi@ð@@ü€@î@ñ@@Žp@@ð@ò@@ý€@ñ@ó@@d@òx@ô@@¤@òi@õ@@´@ð2@ö@@Ê€@å@÷@@Žp@@ö@ø@@É€@÷@ù@@d@øi@ú@@ý€@ø@û@@d@úx@ü@@¤@úi@ý@@Žp€@ö@þ@@É€@ý@ÿ@@d@þiA@@Ê€@þA@@ý@AA@@dAxA@@¤AiA@@ý€AA@@dAyA@@¤AiA@@ˆÇ€@äA@@Ê@AA @@dANA @@É€AA @@dA iA @@ü€A A @@Žp@A A@@ý€A A@@dAxA@@¤AiA@@´A 2A@@ü€AA@@Žp@AA@@É€AA@@dAiA@@ý€AA@@dAxA@@¤AiA@@´A2A*@U0ó70Á-  -@bAlternatively, Mathcad has a built-in function for calculating the y-intercept of a best-fit line.7b9bA@@ý@A=A?@@dA>yA@@@¤A>iAA@@Ê€A=AB@@dAAmAC@@ý€AAAD@@dACxAE@@¤ACiAF@@¤A<bAG@@´A:2AH@@ˆÇ€A9AI@@dAHNAJ@@´AH2AK*@UH›«H¨ÈMÐÐ-'Stdev is the standard deviation of fit.7'9'AL<'AM:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1AN</'AO<'AP0ÿÿÿÿ@NormalArialÿÿÿ AQ@B@UºVÌ"ÈÅAR@@ pAS@@ŒÁ€ARAT@@dASSSAU@@–Ä€ASAV@@+@AU@XAW@@¤AU _n_u_l_l_AX@B@UâXü/øÆAY@@ pAZ@@ Á€AYA[@@dAZstdevA\@@š{€AZA]@@¤A\SSA^@B@U€êÚü¦øÇA_@@ pA`@@ŒÁ€A_Aa@@dA`stdevAb@@–Ä€A`Ac@@+@Ab@XAd@@¤Ab _n_u_l_l_Ae@B@U9íˆ*XÒAf@@ pAg@@ Á€AfAh@@dAgsdmAi@@Ê€AgAj@@dAistdevAk@@š{€AiAl@@û€AkAm@@dAlNAn@@ˆÇ€AlAo@@Ê@AnAp@@dAoNAq@@É€AoAr@@dAqiAs@@ü€AqAt@@Žp@AsAu@@ý€AtAv@@dAuxAw@@¤AuiAx@@´As2Ay@@ü€AnAz@@Žp@AyA{@@É€AzA|@@dA{iA}@@ý€A{A~@@dA}xA@@¤A}iA€@@´Ay2A*@U(S2c(`Ó}  -/Calculates the standard deviation of the slope.7/9/A‚:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1B?</B@<BA0ÿÿÿÿ@NormalArialÿÿÿ BB@B@UˆrÝ„©€BC@@ pBD@@ŒÁ€BCBE@@dBDsdmBF@@–Ä€BDBG@@+@BF@XBH@@¤BF _n_u_l_l_BI*@U“L£ àDD- intercept is 7 9 BJ< BK:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1BL</ BM< BN0ÿÿÿÿ@NormalArialÿÿÿ BO@B@U°’ú¤¿ BP@@ pBQ@@ŒÁ€BPBR@@dBQbBS@@–Ä€BQBT@@+@BS@XBU@@¤BS _n_u_l_l_BV*@U “r£  RR-uncertainty is 79BW<BX:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1BY</BZ<B[0ÿÿÿÿ@NormalArialÿÿÿ B\@B@Uˆ’Ù¤¥ B]@@ pB^@@ŒÁ€B]B_@@dB^sdbB`@@–Ä€B^Ba@@+@B`@XBb@@¤B` _n_u_l_l_Bc*@U»”ËÈUŒŒ-correlation coefficient is 79Bd<Be:@W,ÿÿÿÿÿÿÿÿÿÿÿÿ1Bf</Bg<Bh0ÿÿÿÿ@NormalArialÿÿÿ Bi@B@U°ºöÌÈÈBj@@ pBk@@ŒÁ€BjBl@@dBkR2Bm@@–Ä€BkBn@@+@Bm@XBo@@¤Bm _n_u_l_l_Bp*@U(ë(øÝ0Ý0-@ÅIn lab reports, you should always graph your original x-y data with the best-fit line. To accomplish this, use the slope and y-intercept from above to calculate y-values for each of your x-values.7Å9ÅBq<ÅBr:@Wÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ1Bs</ÅBt<ÅBu0ÿÿÿÿ@NormalArialÿÿÿ Bv@B@U:|L@HBw@@ pBx@@ Á€BwBy@@dBxycalcBz@@‰Ç€BxB{@@Ê@BzB|@@dB{mB}@@¤B{xB~@@¤BzbB*@UÐ;¿KÐHõïï-)Generates an array of calculated y-values7)9)B€<)B:@Wÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ1B‚</)Bƒ<)B„0ÿÿÿÿ@NormalArialÿÿÿ B…*@U¨iã|¨xâ;;-,Plot of Original Data with the Best-Fit Line7,B†<,B‡8B…l Arial9,Bˆ<,B‰:@Wÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ1BŠ</,B‹<,BŒ0ÿÿÿÿ@NormalArialÿÿÿ B@B@U8‡) 8ˆBŽ@@ pB@@Á€BŽB@@ŸÁ@BB‘@@ŸÁ@BB’@@ŸÁ@B‘B“@@vB’3.8B”@@¶B’1.4B•@@ŸÁ€B‘B–@@@B•B—@@€B•B˜@@ ÀBB™@@dB˜yBš@@¤B˜ycalcB›@@ŸÁ€BBœ@@ŸÁ@B›B@@ŸÁ@BœBž@@vB6.3BŸ@@¶B3.9B @@ŸÁ€BœB¡@@@B B¢@@€B B£@@¤B›xB¤ 4 )L)L&&&&&&&&&& & & & & &&&