6. 14.55 [This question is worked out in a team by Liwei He and Sheng Kang]
a) The scatterplots of the variables are shown in the graph below. We can see that
variable 3 and variable 4 (tank vapor pressure and gas vapor pressure) has a very strong
linear relationship. Variable 1 (tank temperature) shows clustered relationship with other
variables. Looking at the last row of the plots, we can see that variable 2, 3 and 4 will be
more important in the model than variable 1, as they have stronger relationship with
variable 5 (emitted hydrocarbon).
From the plots on the diagonal, it can be seen the variables do not spread out well,
therefore transformation may be helpful. Also, there appears to have some outliers as
shown in the plots of column 1 and 2.
b) First regress emitted hydrocarbon against all the other 4 variables, the regression
results are:
Summary of Fit
Rsquare
0.8754
Rsquare Adj
0.8691
Mean Square Error
7.7276
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β
standard error
t
pvalue
constant
0.06433
1.363096421
0.04719
0.962479
TankTemp
0.0821
0.063584053
1.29117
0.2003636
GasTemp
0.209344
0.061409829
3.40896
0.0010239
TankVapor
4.23832
1.927890127
2.19842
0.0308085
GasVapor
9.774285
2.095708436
4.663952
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 Spring '10
 Roy
 Statistics, Normal Distribution, Regression Analysis, Standard Deviation, GasTemp TankVapor GasVapor, adj mean square

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