Quantitative Methods Using more than one explanatory variable.
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Transcript of Quantitative Methods Using more than one explanatory variable.
Quantitative Methods
Using more thanone explanatory variable
Using more than one explanatory variable
Why use more than one?
• Intervening or “3rd” variables (schoolchildren’s maths)• Reducing error variation (saplings)• There is more than one interesting predictor (trees)
Using more than one explanatory variable
Statistical elimination
Using more than one explanatory variable
Statistical elimination
Using more than one explanatory variable
Statistical elimination
Using more than one explanatory variable
Statistical elimination
Using more than one explanatory variable
Statistical elimination
Using more than one explanatory variable
Sequential and Adjusted Sums of Squares
Using more than one explanatory variable
Sequential and Adjusted Sums of Squares
Using more than one explanatory variable
Sequential and Adjusted Sums of Squares
2761.1
Using more than one explanatory variable
Sequential and Adjusted Sums of Squares
Using more than one explanatory variable
Sequential and Adjusted Sums of Squares
Using more than one explanatory variable
Sequential and Adjusted Sums of Squares
Using more than one explanatory variable
Sequential and Adjusted Sums of Squares
Using more than one explanatory variable
Sequential and Adjusted Sums of Squares
MTB > glm lvol=lhgt;SUBC> covar lhgt.
Source DF Seq SS Adj SS Adj MS F PLHGT 1 3.5042 3.5042 3.5042 21.14 0.000Error 29 4.8080 4.8080 0.1658Total 30 8.3122
MTB > glm lvol=lhgt+ldiam;SUBC> covar lhgt ldiam.
Source DF Seq SS Adj SS Adj MS F PLHGT 1 3.5042 0.1987 0.1987 30.14 0.000LDIAM 1 4.6234 4.6234 4.6234 701.33 0.000Error 28 0.1846 0.1846 0.0066Total 30 8.3122
Using more than one explanatory variable
Models and parameters
Using more than one explanatory variable
Models and parameters
Y = +
Unknown quantities we would like to know, in Known quantities that are estimates of them, in Latin
Using more than one explanatory variable
Models and parameters
Y = +
YIELD=μ +
Fertil Coeff
A α1
B α2
C −α1 −α2
⎡
⎣
⎢ ⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥ ⎥
+ε
FINALHT=μ +β ×INITHT+
Water Coeff
A α1
B α2
C α3
D −α1 −α2 −α3
⎡
⎣
⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
+ε
AMA=μ +β ×YEARS+γ ×HGHT+ε
LVOL=μ +β ×LDIAM +γ ×LHGT+ε
WGHT=μ +β ×LLEG+γ ×RLEG+ε
Using more than one explanatory variable
Models and parameters
LVOL=μ +β ×LDIAM +γ ×LHGT+ε
MTB > glm lvol=ldiam+lhgt;SUBC> covar ldiam lhgt.
Analysis of Variance for LVOL, using Adjusted SS for Tests
Source DF Seq SS Adj SS Adj MS F PLDIAM 1 7.9289 4.6234 4.6234 701.33 0.000LHGT 1 0.1987 0.1987 0.1987 30.14 0.000Error 28 0.1846 0.1846 0.0066Total 30 8.3122
Term Coef SE Coef T PConstant -6.6467 0.7983 -8.33 0.000LDIAM 1.98306 0.07488 26.48 0.000LHGT 1.1203 0.2041 5.49 0.000
Using more than one explanatory variable
Models and parametersMTB > glm lvol=ldiam;SUBC> covariate ldiam.
Analysis of Variance for LVOL
Source DF Seq SS Adj SS Adj MS F PLDIAM 1 7.9254 7.9254 7.9254 599.72 0.000Error 29 0.3832 0.3832 0.0132Total 30 8.3087
Using more than one explanatory variable
Models and parametersMTB > glm lvol=ldiam;SUBC> covariate ldiam.
Analysis of Variance for LVOL
Source DF Seq SS Adj SS Adj MS F PLDIAM 1 7.9254 7.9254 7.9254 599.72 0.000Error 29 0.3832 0.3832 0.0132Total 30 8.3087
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QuickTime™ and aAnimation decompressor
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QuickTime™ and aAnimation decompressor
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Source DF Seq SS Adj SS Adj MS F PLDIAM 1 7.9254 7.9254 7.9254 599.72 0.000Error 29 0.3832 0.3832 0.0132Total 30 8.3087
Source DF Seq SS Adj SS Adj MS F PLDIAM 1 7.9254 4.6275 4.6275 698.63 0.000LHEIGHT 1 0.1978 0.1978 0.1978 29.86 0.000Error 28 0.1855 0.1855 0.0066Total 30 8.3087
Using more than one explanatory variable
Models and parameters
Using more than one explanatory variable
Geometry in 3-D
Using more than one explanatory variable
Geometry in 3-D
Source DF Seq SS Adj SS Adj MS F PLHGT 1 3.5042 0.1987 0.1987 30.14 0.000LDIAM 1 4.6234 4.6234 4.6234 701.33 0.000Error 28 0.1846 0.1846 0.0066Total 30 8.3122
Source DF Seq SS Adj SS Adj MS F PLDIAM 1 7.9289 4.6234 4.6234 701.33 0.000LHGT 1 0.1987 0.1987 0.1987 30.14 0.000Error 28 0.1846 0.1846 0.0066Total 30 8.3122
Using more than one explanatory variable
Geometry in 3-D
Using more than one explanatory variable
Geometry in 1-D
Using more than one explanatory variable
Next week: Designing experiments
Read Chapter 5
• Two or more x-variables are often useful and often necessary, and are easy to fit
• Statistical elimination, Seq and Adj SS, plug-in parts• Two variables may duplicate each others’
information (right and left legs)...• ... or they may unmask it (poets’ dates)
Last words…