(15 marks) One study examined the impact of temperature on the viscosity of iven
ID: 3065969 • Letter: #
Question
(15 marks) One study examined the impact of temperature on the viscosity of iven in the following table, where temper toluene-tetralin blends. The data are g ature is measured in °C and viscosity is in mPa-s. Temperature 24.935.044.955.165.275.285.295.2 Viscosity 1.133 0.977 0.853 0.755 0.672 0.602 0.542 0.507 (a) (6 marks) Plot the data and fit the simple linear regression model. Is the linear model a good fit for the data? (Include residual analysis here.) (b) (7 marks) Fit a quadratic model. Present the residual analysis and the fitted model. Also include the scatter plot with fitted quadratic line (c) (2 marks) What proportion of the variation in viscosity can be explained by the quadratic model in (b)?Explanation / Answer
a)
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.980
R Square
0.960
Adjusted R Square
0.954
Standard Error
0.047
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
1
0.325
0.325
144.727
0.000
Residual
6
0.013
0.002
Total
7
0.339
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
1.281
0.047
27.350
0.000
1.167
1.396
Temperature
-0.009
0.001
-12.030
0.000
-0.011
-0.007
RESIDUAL OUTPUT
PROBABILITY OUTPUT
Observation
Predicted Viscosity
Residuals
Standard Residuals
Percentile
Viscosity
1
1.063365838
0.069634162
1.586089461
6.25
0.507
2
0.974890315
0.002109685
0.048053272
18.75
0.542
3
0.888166783
-0.035166783
-0.801010041
31.25
0.602
4
0.798815264
-0.043815264
-0.998000505
43.75
0.672
5
0.710339742
-0.038339742
-0.873281993
56.25
0.755
6
0.622740214
-0.020740214
-0.472409427
68.75
0.853
7
0.535140686
0.006859314
0.156237755
81.25
0.977
8
0.447541159
0.059458841
1.354321478
93.75
1.133
b)
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.9996
R Square
0.9992
Adjusted R Square
0.9989
Standard Error
0.0071
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
2
0.339
0.169
3319.530
0.000
Residual
5
0.000
0.000
Total
7
0.339
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
1.553
0.018
85.082
0.000
1.506
1.599
Temperature
-0.019
0.001
-29.040
0.000
-0.021
-0.018
Temperature^2
0.000
0.000
16.108
0.000
0.000
0.000
RESIDUAL OUTPUT
PROBABILITY OUTPUT
Observation
Predicted Viscosity
Residuals
Standard Residuals
Percentile
Viscosity
1
1.125549253
0.007450747
1.23429054
6.25
0.507
2
0.983492198
-0.006492198
-1.075497339
18.75
0.542
3
0.861693737
-0.008693737
-1.440204122
31.25
0.602
4
0.75426852
0.00073148
0.121176988
43.75
0.672
5
0.665961479
0.006038521
1.000341101
56.25
0.755
6
0.596238675
0.005761325
0.954420854
68.75
0.853
7
0.544137671
-0.002137671
-0.354126512
81.25
0.977
8
0.509658467
-0.002658467
-0.440401509
93.75
1.133
c)
99.92% of the variation in viscosity is explained for by in the quadratic model.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.980
R Square
0.960
Adjusted R Square
0.954
Standard Error
0.047
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
1
0.325
0.325
144.727
0.000
Residual
6
0.013
0.002
Total
7
0.339
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
1.281
0.047
27.350
0.000
1.167
1.396
Temperature
-0.009
0.001
-12.030
0.000
-0.011
-0.007
RESIDUAL OUTPUT
PROBABILITY OUTPUT
Observation
Predicted Viscosity
Residuals
Standard Residuals
Percentile
Viscosity
1
1.063365838
0.069634162
1.586089461
6.25
0.507
2
0.974890315
0.002109685
0.048053272
18.75
0.542
3
0.888166783
-0.035166783
-0.801010041
31.25
0.602
4
0.798815264
-0.043815264
-0.998000505
43.75
0.672
5
0.710339742
-0.038339742
-0.873281993
56.25
0.755
6
0.622740214
-0.020740214
-0.472409427
68.75
0.853
7
0.535140686
0.006859314
0.156237755
81.25
0.977
8
0.447541159
0.059458841
1.354321478
93.75
1.133
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.