.MCAD 303010000 1 74 21 0 .CMD PLOTFORMAT 0 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 0 NO-TRACE-STRING 0 2 1 0 NO-TRACE-STRING 0 3 2 0 NO-TRACE-STRING 0 4 3 0 NO-TRACE-STRING 0 1 4 0 NO-TRACE-STRING 0 2 5 0 NO-TRACE-STRING 0 3 6 0 NO-TRACE-STRING 0 4 0 0 NO-TRACE-STRING 0 1 1 0 NO-TRACE-STRING 0 2 2 0 NO-TRACE-STRING 0 3 3 0 NO-TRACE-STRING 0 4 4 0 NO-TRACE-STRING 0 1 5 0 NO-TRACE-STRING 0 2 6 0 NO-TRACE-STRING 0 3 0 0 NO-TRACE-STRING 0 4 1 0 NO-TRACE-STRING 0 1 21 15 0 3 .CMD FORMAT rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge temperature tr=0 vm=0 .CMD SET ORIGIN 0 .CMD SET TOL 0.001000000000000 .CMD SET PRNCOLWIDTH 8 .CMD SET PRNPRECISION 4 .CMD PRINT_SETUP 1.200000 0.983333 1.200000 1.200000 0 .CMD HEADER_FOOTER 1 1 *empty* *empty* *empty* 0 1 *empty* *empty* *empty* .CMD HEADER_FOOTER_FONT fontID=14 family=Arial points=10 bold=0 italic=0 underline=0 .CMD HEADER_FOOTER_FONT fontID=15 family=Arial points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE_NAME fontID=0 name=Variables .CMD DEFINE_FONTSTYLE_NAME fontID=1 name=Constants .CMD DEFINE_FONTSTYLE_NAME fontID=2 name=Text .CMD DEFINE_FONTSTYLE_NAME fontID=4 name=User^1 .CMD DEFINE_FONTSTYLE_NAME fontID=5 name=User^2 .CMD DEFINE_FONTSTYLE_NAME fontID=6 name=User^3 .CMD DEFINE_FONTSTYLE_NAME fontID=7 name=User^4 .CMD DEFINE_FONTSTYLE_NAME fontID=8 name=User^5 .CMD DEFINE_FONTSTYLE_NAME fontID=9 name=User^6 .CMD DEFINE_FONTSTYLE_NAME fontID=10 name=User^7 .CMD DEFINE_FONTSTYLE fontID=0 family=Times^New^Roman points=12 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=1 family=Times^New^Roman points=12 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=2 family=Times^New^Roman points=12 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=4 family=Arial points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=5 family=Courier^New points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=6 family=System points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=7 family=Script points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=8 family=Roman points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=9 family=Modern points=10 bold=0 italic=0 underline=0 .CMD DEFINE_FONTSTYLE fontID=10 family=Times^New^Roman points=10 bold=0 italic=0 underline=0 .CMD UNITS U=1 .CMD DIMENSIONS_ANALYSIS 0 0 .TXT 3 1 17 0 Cg b73.000000,73.000000,1089 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} {\f3\fnil Symbol;} {\f4\fnil Century Gothic;} } {\plain {\b \fs28 Linear Regression\par \par }{\b0 \fs28 \i \fs24 Zoran Zdravkovski, Institute of Chemistry, Skopje, Macedoni}{\b0 \fs28 \i \fs24 a}{\fs28 \b }{\par \par In the spectrophotometric determination of manganese (as permanganate) a linear dependence of the absorbance for a given concentration range is obtanied: \par \par }{\i c}{/(mmol/L) 0.186 0.459 0.728 0.906 1.094 1.351 1.647 1.838\par }{\i A }{ 0.092 0.202 0.321 0.401 0.498 0.602 0.731 0.820\par \par The formula for this linear dependence can be written as }{\b \i y=b*x+a}{, where }{\b \i y}{ corresponds to the absorbance and }{\i \b x}{ to the concentration (or }{\i \b A=b*c+a}{). The parameters }{\i \b b}{ and }{\i \b a}{, are the slope of the line and the intercept with the ordinate, respectively.\par In Mathcad, the data series are defined as vectors (one-column matrices). The syntax for the slope and the intercept, as well as the correlation of the two sets of data is simple (plain English), as illustrated in the following example: }} } .EQN 51 3 1 0 {0:c}NAME:({8,1}1.8381.6471.3511.0940.9060.7280.4590.186) .EQN 0 18 2 0 {0:A}NAME:({8,1}0.8200.7310.6020.4980.4010.3210.2020.092) .EQN 9 16 8 0 {0:i}NAME:0;{0:last}NAME({0:c}NAME) .EQN 7 -35 3 0 {0:b}NAME:{0:slope}NAME({0:c}NAME,{0:A}NAME) .EQN 0 21 5 0 {0:a}NAME:{0:intercept}NAME({0:c}NAME,{0:A}NAME) .EQN 3 -21 4 0 {0:b}NAME={0}?_n_u_l_l_ .EQN 0 21 6 0 {0:a}NAME={0}?_n_u_l_l_ .TXT 4 -9 12 0 Cg a26.500000,68.000000,37 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} {\f3\fnil Symbol;} {\f4\fnil Century Gothic;} } {\plain {The regression line is as follows:}} } .EQN 0 30 7 0 ({0:yr}NAME)[({0:i}NAME):{0:b}NAME*({0:c}NAME)[({0:i}NAME)+{0:a}NAME .EQN 2 -30 9 0 _n_u_l_l_&_n_u_l_l_&(_n_u_l_l_&_n_u_l_l_)&({0:yr}NAME)[({0:i}NAME),({0:A}NAME)[({0:i}NAME)@_n_u_l_l_&_n_u_l_l_&(_n_u_l_l_&_n_u_l_l_)&({0:c}NAME)[({0:i}NAME) 0 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 0 NO-TRACE-STRING 1 0 1 0 NO-TRACE-STRING 0 3 2 0 NO-TRACE-STRING 0 4 3 0 NO-TRACE-STRING 0 1 4 0 NO-TRACE-STRING 0 2 5 0 NO-TRACE-STRING 0 3 6 0 NO-TRACE-STRING 0 4 0 0 NO-TRACE-STRING 0 1 1 0 NO-TRACE-STRING 0 2 2 0 NO-TRACE-STRING 0 3 3 0 NO-TRACE-STRING 0 4 4 0 NO-TRACE-STRING 0 1 5 0 NO-TRACE-STRING 0 2 6 0 NO-TRACE-STRING 0 3 0 0 NO-TRACE-STRING 0 4 1 0 NO-TRACE-STRING 0 1 35 16 0 3 .TXT 30 -14 18 0 Cg a69.600000,71.800000,167 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} {\f3\fnil Symbol;} {\f4\fnil Century Gothic;} } {\plain { The calibration curve (regression line) can be used to determine the concentration of unknown samples (that's why we construct it in the first place, anyway):}} } .TXT 11 0 19 0 Cg a14.500000,72.000000,19 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} {\f3\fnil Symbol;} {\f4\fnil Century Gothic;} } {\plain {unknown samples:}} } .TXT 0 42 20 0 Cg a20.200000,36.000000,28 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} {\f3\fnil Symbol;} {\f4\fnil Century Gothic;} } {\plain {concentration of samples:}} } .EQN 7 -36 13 0 {0:Ax}NAME:({3,1}0.9500.2380.120) .EQN 0 25 14 0 {0:cx}NAME:({0:Ax}NAME-{0:a}NAME)/({0:b}NAME) .EQN 0 25 15 0 {0:cx}NAME={0}?_n_u_l_l_ .TXT 7 -56 16 0 Cg a67.100000,67.000000,442 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} {\f3\fnil Symbol;} {\f4\fnil Century Gothic;} } {\plain { The last value for the concentration of 2.135 mmol/L is outside the range used for the calibration curve (0.186-1.838 mmol/L), indicating that the range of the calibration curve was not properly chosen. However, in this case, the correlation coefficient is very high, and the point in question is not too far from the range that with high degree of confidence this extrapolation can give acceptable values for the concentration.}} } .TXT 19 0 21 0 Cg a70.300000,71.000000,422 {\rtf1\ansi \deff2 {\fonttbl {\f0\fnil Arial;} {\f1\fnil Courier;} {\f2\fnil Times New Roman;} {\f3\fnil Symbol;} {\f4\fnil Century Gothic;} } {\plain {\b References}{:\par \par 1. Z. Zdravkovski, Mathcad in Chemistry Calculations, }{\i J. Chem. Ed.}{ }{\b 1991}{, }{\i 68}{, A95 and }{\b 1992}{, }{\i 69}{, A240.\par \par 2. T. R. Dickson, The Computer and Chemistry, W. H. Freeman, San Francisco, 1968 .\par \par 3. P. W. Atkins, Physical Chemistry, W. H. Freeman, New York, 4th Ed., 1990.\par \par 4. J. Freund, Modern Elementary Statistics, Prentice-Hall, Englewood Cliffs, 1979.\par \par }} }