sla: Two-Group, Straight-Line ANCOVA: Four Models
In sla: Two-Group Straight Line ANCOVA
Description
Usage
Arguments
Value
Note
Author(s)
References
Examples
Description
Fits four linear models ("A", "B", "C", and "D") for the two-group, straight-line ANCOVA problem. (A) Model "A", the full model - fits two intercepts and two slopes (separate intercepts and slopes for each group); (B) Model "B", a reduced model - fits single intercept and single slope to all the data (ignoring group designation); (C) Model "C", a reduced model - fits two different intercepts and a single, common slope; (D) Model "D", a reduced model - fits a single, common intercept and two different slopes.
Usage
1
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9
Arguments
facxy
a data frame with three columns in specific order: (1) factor (Group) variable, (2) numeric x-axis predictor, regressor (or independent) variable, and (3) numeric y-axis criterion (or dependent) variable.
x
an object of class 'sla', i.e., a list containing data frames, coefficients, and fitted models.
object
an object of class 'sla', i.e., a list containing data frames, coefficients, and fitted models.
modelType2Plot
a character letter, "A", "B", "C", or "D", to indicate which model, with its associated fitted lines (abline), to plot.
...
not used.
Value
Returns an object of class "sla", which is a list containing the following components:
Call
model call
INPUT.df
input data frame
Summary of Input Data Frame
produced from the generic function summary().
Mod.A
an object of class "lm" for the fit of Model A.
Mod.B
an object of class "lm" for the fit of Model B.
Mod.C
an object of class "lm" for the fit of Model C.
Mod.D
an object of class "lm" for the fit of Model D.
Fit.Table
a data frame containing a description of the fit, number of parameters estimated, residual degrees of freedom, residual sum of squares, and residual mean square for each model "lm" fit, i.e., for models A, B, C and D.
Test.Table
a data frame containing a description of three tests of (reduced) models B, C, and D vs. the (full) model A, the degrees of freedom associated with the anova() comparison of the reduced and full models [note: always 2, 1, and 1], the difference between the residual sums of squares between the reduced and full models, the F statistic associated with the test, and the probability associated with the corresponding F statistic for the test.
Fit.Table.Pretty
a data frame containing essentially the same information as in Fit.Table but displayed in a prettier format.
Test.Table.Pretty
a data frame containing essentially the same information as in Test.Table but displayed in a prettier format.
Note
(1) The hellung data frame with conc and diameter raw values is available in the ISwR library from Dalgaard P (2002) Introductory Statistics with R. Springer.
(2) Simulated data sets (without setting the seed) using the code provided in the examples yield the desired outcomes 95 percent of the time.
Author(s)
W Greg Alvord
References
Dalgaard P (2002) Introductory Statistics with R. Springer.
Draper NR and Smith H (1998) Applied Regression Analysis. 3rd ed. Wiley.
Fox J (2008) Applied Regression Analysis and General Linear Models, 2nd ed. Sage.
Fox J and Weisberg S (2011) An R Companion to Applied Regression, 2nd ed. Sage.
Searle SR (1971) Linear Models, Wiley.
Venables WN and Ripley BD (2002) Modern Applied Statistics with S. 4th ed. Springer.
Examples
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data(eqslo)
eqsloObj <- sla(eqslo)
eqsloObj
summary(eqsloObj)
attributes(eqsloObj)
eqsloObj$Mod.C # best fitting reduced model, equivalent slopes, different intercepts
summary(eqsloObj$Mod.C) # lm summary of Model C
plot(eqsloObj, mod = 'C') # plot of data eqslo, fitted lines with equal slopes, different intercepts
##
data(eqint)
eqintObj <- sla(eqint)
eqintObj
summary(eqintObj)
attributes(eqintObj)
eqintObj$Mod.D # best fitting reduced model, equivalent intercepts, different slopes
summary(eqintObj$Mod.D) # lm summary of Model D
plot(eqintObj, mod = 'D') # plot of data eqint, fitted lines with equal intercepts, different slopes
##
## See MASS, 4th ed., pp 139-144 for ANCOVA of whiteside data
##
library(MASS)
data(whiteside)
whitesideObj <- sla(whiteside)
summary(whitesideObj) # See MASS, 4th ed., pp 139-144 for ANCOVA of whiteside data
par(mfrow = c(2,2))
plot(whitesideObj, "A") # different intercepts and different slopes
plot(whitesideObj, "B") # common intercept and common slope
plot(whitesideObj, "C") # different intercepts, common slope
plot(whitesideObj, "D") # different slopes, common intercept
##
## See Dalgaard, pp. 172-182 for ANCOVA of (log10) hellung data
##
data(hellunglog)
hellunglogObj <- sla(hellunglog)
hellunglogObj
summary(hellunglogObj) # See Dalgaard, pp. 172-182 for ANCOVA of (log10) hellung data
par(mfrow = c(2,2))
plot(hellunglogObj, "A") # different intercepts and different slopes
plot(hellunglogObj, "B") # common intercept and common slope
plot(hellunglogObj, "C") # different intercepts, common slope
plot(hellunglogObj, "D") # different slopes, common intercept
##
## Simulate data for common slope, different intercepts
##
group <- c(rep('A', 50), rep('B', 50))
x <- rep(1:50, 2)
set.seed(50) #
y1 <- rnorm(50) + 4*.05*x[1:50]
set.seed(100)
y2 <- rnorm(50) + 7 + y1
y <- c(y1, y2)
esdf <- data.frame(group, x, y)
esdfObj <- sla(esdf)
esdfObj
summary(esdfObj)
par(mfrow = c(2,2))
plot(esdfObj, mod = 'A')
plot(esdfObj, mod = 'B')
plot(esdfObj, mod = 'C')
plot(esdfObj, mod = 'D')
##
## Simulate data for common intercept, different slopes
##
group <- c(rep('A', 50), rep('B', 50))
x <- rep(1:50, 2)
set.seed(49) #
y1 <- rnorm(50) + 1*.03*x[1:50]
set.seed(99) #
y2 <- rnorm(50) + 1*.25*x[51:100]
y <- c(y1, y2)
eidf <- data.frame(group, x, y)
eidfObj <- sla(eidf)
eidfObj
summary(eidfObj)
par(mfrow = c(2,2))
plot(eidfObj, mod = 'A')
plot(eidfObj, mod = 'B')
plot(eidfObj, mod = 'C')
plot(eidfObj, mod = 'D')
Example output
Call: sla.default(facxy = eqslo)
Coefficients for Models A, B, C and D:
Model A:
Int_1 Slo_1 Int_2 Slo_2
1.2 2.6 11.6 2.4
Model B:
Com_Int Com_Slo
6.4 2.5
Model C:
Int_1 Int_2 Com_Slo
1.5 11.3 2.5
Model D:
Com_Int Slo_1 Slo_2
6.400000 1.181818 3.818182
Call: sla.default(facxy = eqslo)
Summary of ANCOVA Tests. . .
Description of Fits for 4 ANCOVA Models
Description of Fit Np Res df Res SS Res MS
1 Mod A: Ind I,Ind S 4 6 3.60 0.60
2 Mod B: Com I,Com S 2 8 243.90 30.49
3 Mod C: Ind I,Com S 3 7 3.80 0.54
4 Mod D: Com I,Ind S 3 7 52.76 7.54
ANCOVA Tests: Two Groups/Straight Line Fits
Test df SS F Stat prob
1 Ho: Equiv D.Sets 2 240.30 200.25 0.0000
2 Ho: Equiv Slopes 1 0.20 0.33 0.5847
3 Ho: Equiv Inters 1 49.16 81.94 0.0001
$names
[1] "Call" "INPUT.df"
[3] "Summary of Input Data Frame" "Mod.A"
[5] "Mod.B" "Mod.C"
[7] "Mod.D" "Fit.Table"
[9] "Test.Table" "Fit.Table.Pretty"
[11] "Test.Table.Pretty"
$class
[1] "sla"
Call:
lm(formula = y ~ X.C - 1)
Coefficients:
X.Ci1 X.Ci2 X.Cx
1.5 11.3 2.5
Call:
lm(formula = y ~ X.C - 1)
Residuals:
Min 1Q Median 3Q Max
-1.000 -0.450 0.100 0.425 1.000
Coefficients:
Estimate Std. Error t value Pr(>|t|)
X.Ci1 1.5000 0.5940 2.525 0.0395 *
X.Ci2 11.3000 0.5940 19.023 2.76e-07 ***
X.Cx 2.5000 0.1648 15.174 1.30e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.7368 on 7 degrees of freedom
Multiple R-squared: 0.9983, Adjusted R-squared: 0.9976
F-statistic: 1411 on 3 and 7 DF, p-value: 4.259e-10
Call: sla.default(facxy = eqint)
Coefficients for Models A, B, C and D:
Model A:
Int_1 Slo_1 Int_2 Slo_2
1.20 2.60 1.06 -0.02
Model B:
Com_Int Com_Slo
1.13 1.29
Model C:
Int_1 Int_2 Com_Slo
5.13 -2.87 1.29
Model D:
Com_Int Slo_1 Slo_2
1.13000000 2.61909091 -0.03909091
Call: sla.default(facxy = eqint)
Summary of ANCOVA Tests. . .
Description of Fits for 4 ANCOVA Models
Description of Fit Np Res df Res SS Res MS
1 Mod A: Ind I,Ind S 4 6 2.44 0.41
2 Mod B: Com I,Com S 2 8 196.76 24.59
3 Mod C: Ind I,Com S 3 7 36.76 5.25
4 Mod D: Com I,Ind S 3 7 2.44 0.35
ANCOVA Tests: Two Groups/Straight Line Fits
Test df SS F Stat prob
1 Ho: Equiv D.Sets 2 194.32 239.31 0.0000
2 Ho: Equiv Slopes 1 34.32 84.54 0.0001
3 Ho: Equiv Inters 1 0.01 0.02 0.8871
$names
[1] "Call" "INPUT.df"
[3] "Summary of Input Data Frame" "Mod.A"
[5] "Mod.B" "Mod.C"
[7] "Mod.D" "Fit.Table"
[9] "Test.Table" "Fit.Table.Pretty"
[11] "Test.Table.Pretty"
$class
[1] "sla"
Call:
lm(formula = y ~ X.D - 1)
Coefficients:
X.D X.Di1x X.Di2x
1.13000 2.61909 -0.03909
Call:
lm(formula = y ~ X.D - 1)
Residuals:
Min 1Q Median 3Q Max
-0.98727 -0.10727 0.00682 0.21977 0.77455
Coefficients:
Estimate Std. Error t value Pr(>|t|)
X.D 1.13000 0.43829 2.578 0.0366 *
X.Di1x 2.61909 0.14366 18.231 3.7e-07 ***
X.Di2x -0.03909 0.14366 -0.272 0.7934
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.591 on 7 degrees of freedom
Multiple R-squared: 0.9949, Adjusted R-squared: 0.9927
F-statistic: 455.8 on 3 and 7 DF, p-value: 2.191e-08
Call: sla.default(facxy = whiteside)
Summary of ANCOVA Tests. . .
Description of Fits for 4 ANCOVA Models
Description of Fit Np Res df Res SS Res MS
1 Mod A: Ind I,Ind S 4 52 5.43 0.10
2 Mod B: Com I,Com S 2 54 39.99 0.74
3 Mod C: Ind I,Com S 3 53 6.77 0.13
4 Mod D: Com I,Ind S 3 53 20.02 0.38
ANCOVA Tests: Two Groups/Straight Line Fits
Test df SS F Stat prob
1 Ho: Equiv D.Sets 2 34.57 165.67 0e+00
2 Ho: Equiv Slopes 1 1.35 12.89 7e-04
3 Ho: Equiv Inters 1 14.59 139.88 0e+00
Call: sla.default(facxy = hellunglog)
Coefficients for Models A, B, C and D:
Model A:
Int_1 Slo_1 Int_2 Slo_2
1.63134359 -0.05319626 1.63476114 -0.05967671
Model B:
Com_Int Com_Slo
1.62731289 -0.05451464
Model C:
Int_1 Int_2 Com_Slo
1.6421324 1.6138945 -0.0553927
Model D:
Com_Int Slo_1 Slo_2
1.63251608 -0.05343178 -0.05922119
Call: sla.default(facxy = hellunglog)
Summary of ANCOVA Tests. . .
Description of Fits for 4 ANCOVA Models
Description of Fit Np Res df Res SS Res MS
1 Mod A: Ind I,Ind S 4 47 0.00 0
2 Mod B: Com I,Com S 2 49 0.01 0
3 Mod C: Ind I,Com S 3 48 0.00 0
4 Mod D: Com I,Ind S 3 48 0.00 0
ANCOVA Tests: Two Groups/Straight Line Fits
Test df SS F Stat prob
1 Ho: Equiv D.Sets 2 0.01 58.75 0.0000
2 Ho: Equiv Slopes 1 0.00 1.81 0.1853
3 Ho: Equiv Inters 1 0.00 0.02 0.8859
Call: sla.default(facxy = esdf)
Coefficients for Models A, B, C and D:
Model A:
Int_1 Slo_1 Int_2 Slo_2
-0.08734404 0.19831531 6.97037298 0.19924832
Model B:
Com_Int Com_Slo
3.4415145 0.1987818
Model C:
Int_1 Int_2 Com_Slo
-0.0992400 6.9822689 0.1987818
Model D:
Com_Int Slo_1 Slo_2
3.44151447 0.09349773 0.30406590
Call: sla.default(facxy = esdf)
Summary of ANCOVA Tests. . .
Description of Fits for 4 ANCOVA Models
Description of Fit Np Res df Res SS Res MS
1 Mod A: Ind I,Ind S 4 96 115.51 1.20
2 Mod B: Com I,Com S 2 98 1369.21 13.97
3 Mod C: Ind I,Com S 3 97 115.51 1.19
4 Mod D: Com I,Ind S 3 97 417.58 4.30
ANCOVA Tests: Two Groups/Straight Line Fits
Test df SS F Stat prob
1 Ho: Equiv D.Sets 2 1253.70 520.98 0.0000
2 Ho: Equiv Slopes 1 0.00 0.00 0.9512
3 Ho: Equiv Inters 1 302.07 251.05 0.0000
Call: sla.default(facxy = eidf)
Coefficients for Models A, B, C and D:
Model A:
Int_1 Slo_1 Int_2 Slo_2
0.03787834 0.02713860 -0.07378883 0.24299515
Model B:
Com_Int Com_Slo
-0.01795525 0.13506688
Model C:
Int_1 Int_2 Com_Slo
-2.7142926 2.6783821 0.1350669
Model D:
Com_Int Slo_1 Slo_2
-0.01795525 0.02879703 0.24133672
Call: sla.default(facxy = eidf)
Summary of ANCOVA Tests. . .
Description of Fits for 4 ANCOVA Models
Description of Fit Np Res df Res SS Res MS
1 Mod A: Ind I,Ind S 4 96 120.87 1.26
2 Mod B: Com I,Com S 2 98 1090.48 11.13
3 Mod C: Ind I,Com S 3 97 363.45 3.75
4 Mod D: Com I,Ind S 3 97 120.95 1.25
ANCOVA Tests: Two Groups/Straight Line Fits
Test df SS F Stat prob
1 Ho: Equiv D.Sets 2 969.60 385.04 0.0000
2 Ho: Equiv Slopes 1 242.58 192.66 0.0000
3 Ho: Equiv Inters 1 0.08 0.06 0.8069
sla documentation built on May 30, 2017, 2:39 a.m.
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Description Usage Arguments Value Note Author(s) References Examples
Description
Fits four linear models ("A", "B", "C", and "D") for the two-group, straight-line ANCOVA problem. (A) Model "A", the full model - fits two intercepts and two slopes (separate intercepts and slopes for each group); (B) Model "B", a reduced model - fits single intercept and single slope to all the data (ignoring group designation); (C) Model "C", a reduced model - fits two different intercepts and a single, common slope; (D) Model "D", a reduced model - fits a single, common intercept and two different slopes.
Usage
1 2 3 4 5 6 7 8 9 |
Arguments
facxy |
a data frame with three columns in specific order: (1) factor (Group) variable, (2) numeric x-axis predictor, regressor (or independent) variable, and (3) numeric y-axis criterion (or dependent) variable. |
x |
an object of class |
object |
an object of class |
modelType2Plot |
a character letter, "A", "B", "C", or "D", to indicate which model, with its associated fitted lines (abline), to plot. |
... |
not used. |
Value
Returns an object of class "sla", which is a list containing the following components:
Call |
model call |
INPUT.df |
input data frame |
Summary of Input Data Frame |
produced from the generic function summary(). |
Mod.A |
an object of class "lm" for the fit of Model A. |
Mod.B |
an object of class "lm" for the fit of Model B. |
Mod.C |
an object of class "lm" for the fit of Model C. |
Mod.D |
an object of class "lm" for the fit of Model D. |
Fit.Table |
a data frame containing a description of the fit, number of parameters estimated, residual degrees of freedom, residual sum of squares, and residual mean square for each model "lm" fit, i.e., for models A, B, C and D. |
Test.Table |
a data frame containing a description of three tests of (reduced) models B, C, and D vs. the (full) model A, the degrees of freedom associated with the anova() comparison of the reduced and full models [note: always 2, 1, and 1], the difference between the residual sums of squares between the reduced and full models, the F statistic associated with the test, and the probability associated with the corresponding F statistic for the test. |
Fit.Table.Pretty |
a data frame containing essentially the same information as in Fit.Table but displayed in a prettier format. |
Test.Table.Pretty |
a data frame containing essentially the same information as in Test.Table but displayed in a prettier format. |
Note
(1) The hellung data frame with conc and diameter raw values is available in the ISwR library from Dalgaard P (2002) Introductory Statistics with R. Springer.
(2) Simulated data sets (without setting the seed) using the code provided in the examples yield the desired outcomes 95 percent of the time.
Author(s)
W Greg Alvord
References
Dalgaard P (2002) Introductory Statistics with R. Springer.
Draper NR and Smith H (1998) Applied Regression Analysis. 3rd ed. Wiley.
Fox J (2008) Applied Regression Analysis and General Linear Models, 2nd ed. Sage.
Fox J and Weisberg S (2011) An R Companion to Applied Regression, 2nd ed. Sage.
Searle SR (1971) Linear Models, Wiley.
Venables WN and Ripley BD (2002) Modern Applied Statistics with S. 4th ed. Springer.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 | data(eqslo)
eqsloObj <- sla(eqslo)
eqsloObj
summary(eqsloObj)
attributes(eqsloObj)
eqsloObj$Mod.C # best fitting reduced model, equivalent slopes, different intercepts
summary(eqsloObj$Mod.C) # lm summary of Model C
plot(eqsloObj, mod = 'C') # plot of data eqslo, fitted lines with equal slopes, different intercepts
##
data(eqint)
eqintObj <- sla(eqint)
eqintObj
summary(eqintObj)
attributes(eqintObj)
eqintObj$Mod.D # best fitting reduced model, equivalent intercepts, different slopes
summary(eqintObj$Mod.D) # lm summary of Model D
plot(eqintObj, mod = 'D') # plot of data eqint, fitted lines with equal intercepts, different slopes
##
## See MASS, 4th ed., pp 139-144 for ANCOVA of whiteside data
##
library(MASS)
data(whiteside)
whitesideObj <- sla(whiteside)
summary(whitesideObj) # See MASS, 4th ed., pp 139-144 for ANCOVA of whiteside data
par(mfrow = c(2,2))
plot(whitesideObj, "A") # different intercepts and different slopes
plot(whitesideObj, "B") # common intercept and common slope
plot(whitesideObj, "C") # different intercepts, common slope
plot(whitesideObj, "D") # different slopes, common intercept
##
## See Dalgaard, pp. 172-182 for ANCOVA of (log10) hellung data
##
data(hellunglog)
hellunglogObj <- sla(hellunglog)
hellunglogObj
summary(hellunglogObj) # See Dalgaard, pp. 172-182 for ANCOVA of (log10) hellung data
par(mfrow = c(2,2))
plot(hellunglogObj, "A") # different intercepts and different slopes
plot(hellunglogObj, "B") # common intercept and common slope
plot(hellunglogObj, "C") # different intercepts, common slope
plot(hellunglogObj, "D") # different slopes, common intercept
##
## Simulate data for common slope, different intercepts
##
group <- c(rep('A', 50), rep('B', 50))
x <- rep(1:50, 2)
set.seed(50) #
y1 <- rnorm(50) + 4*.05*x[1:50]
set.seed(100)
y2 <- rnorm(50) + 7 + y1
y <- c(y1, y2)
esdf <- data.frame(group, x, y)
esdfObj <- sla(esdf)
esdfObj
summary(esdfObj)
par(mfrow = c(2,2))
plot(esdfObj, mod = 'A')
plot(esdfObj, mod = 'B')
plot(esdfObj, mod = 'C')
plot(esdfObj, mod = 'D')
##
## Simulate data for common intercept, different slopes
##
group <- c(rep('A', 50), rep('B', 50))
x <- rep(1:50, 2)
set.seed(49) #
y1 <- rnorm(50) + 1*.03*x[1:50]
set.seed(99) #
y2 <- rnorm(50) + 1*.25*x[51:100]
y <- c(y1, y2)
eidf <- data.frame(group, x, y)
eidfObj <- sla(eidf)
eidfObj
summary(eidfObj)
par(mfrow = c(2,2))
plot(eidfObj, mod = 'A')
plot(eidfObj, mod = 'B')
plot(eidfObj, mod = 'C')
plot(eidfObj, mod = 'D')
|
Example output
Call: sla.default(facxy = eqslo)
Coefficients for Models A, B, C and D:
Model A:
Int_1 Slo_1 Int_2 Slo_2
1.2 2.6 11.6 2.4
Model B:
Com_Int Com_Slo
6.4 2.5
Model C:
Int_1 Int_2 Com_Slo
1.5 11.3 2.5
Model D:
Com_Int Slo_1 Slo_2
6.400000 1.181818 3.818182
Call: sla.default(facxy = eqslo)
Summary of ANCOVA Tests. . .
Description of Fits for 4 ANCOVA Models
Description of Fit Np Res df Res SS Res MS
1 Mod A: Ind I,Ind S 4 6 3.60 0.60
2 Mod B: Com I,Com S 2 8 243.90 30.49
3 Mod C: Ind I,Com S 3 7 3.80 0.54
4 Mod D: Com I,Ind S 3 7 52.76 7.54
ANCOVA Tests: Two Groups/Straight Line Fits
Test df SS F Stat prob
1 Ho: Equiv D.Sets 2 240.30 200.25 0.0000
2 Ho: Equiv Slopes 1 0.20 0.33 0.5847
3 Ho: Equiv Inters 1 49.16 81.94 0.0001
$names
[1] "Call" "INPUT.df"
[3] "Summary of Input Data Frame" "Mod.A"
[5] "Mod.B" "Mod.C"
[7] "Mod.D" "Fit.Table"
[9] "Test.Table" "Fit.Table.Pretty"
[11] "Test.Table.Pretty"
$class
[1] "sla"
Call:
lm(formula = y ~ X.C - 1)
Coefficients:
X.Ci1 X.Ci2 X.Cx
1.5 11.3 2.5
Call:
lm(formula = y ~ X.C - 1)
Residuals:
Min 1Q Median 3Q Max
-1.000 -0.450 0.100 0.425 1.000
Coefficients:
Estimate Std. Error t value Pr(>|t|)
X.Ci1 1.5000 0.5940 2.525 0.0395 *
X.Ci2 11.3000 0.5940 19.023 2.76e-07 ***
X.Cx 2.5000 0.1648 15.174 1.30e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.7368 on 7 degrees of freedom
Multiple R-squared: 0.9983, Adjusted R-squared: 0.9976
F-statistic: 1411 on 3 and 7 DF, p-value: 4.259e-10
Call: sla.default(facxy = eqint)
Coefficients for Models A, B, C and D:
Model A:
Int_1 Slo_1 Int_2 Slo_2
1.20 2.60 1.06 -0.02
Model B:
Com_Int Com_Slo
1.13 1.29
Model C:
Int_1 Int_2 Com_Slo
5.13 -2.87 1.29
Model D:
Com_Int Slo_1 Slo_2
1.13000000 2.61909091 -0.03909091
Call: sla.default(facxy = eqint)
Summary of ANCOVA Tests. . .
Description of Fits for 4 ANCOVA Models
Description of Fit Np Res df Res SS Res MS
1 Mod A: Ind I,Ind S 4 6 2.44 0.41
2 Mod B: Com I,Com S 2 8 196.76 24.59
3 Mod C: Ind I,Com S 3 7 36.76 5.25
4 Mod D: Com I,Ind S 3 7 2.44 0.35
ANCOVA Tests: Two Groups/Straight Line Fits
Test df SS F Stat prob
1 Ho: Equiv D.Sets 2 194.32 239.31 0.0000
2 Ho: Equiv Slopes 1 34.32 84.54 0.0001
3 Ho: Equiv Inters 1 0.01 0.02 0.8871
$names
[1] "Call" "INPUT.df"
[3] "Summary of Input Data Frame" "Mod.A"
[5] "Mod.B" "Mod.C"
[7] "Mod.D" "Fit.Table"
[9] "Test.Table" "Fit.Table.Pretty"
[11] "Test.Table.Pretty"
$class
[1] "sla"
Call:
lm(formula = y ~ X.D - 1)
Coefficients:
X.D X.Di1x X.Di2x
1.13000 2.61909 -0.03909
Call:
lm(formula = y ~ X.D - 1)
Residuals:
Min 1Q Median 3Q Max
-0.98727 -0.10727 0.00682 0.21977 0.77455
Coefficients:
Estimate Std. Error t value Pr(>|t|)
X.D 1.13000 0.43829 2.578 0.0366 *
X.Di1x 2.61909 0.14366 18.231 3.7e-07 ***
X.Di2x -0.03909 0.14366 -0.272 0.7934
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.591 on 7 degrees of freedom
Multiple R-squared: 0.9949, Adjusted R-squared: 0.9927
F-statistic: 455.8 on 3 and 7 DF, p-value: 2.191e-08
Call: sla.default(facxy = whiteside)
Summary of ANCOVA Tests. . .
Description of Fits for 4 ANCOVA Models
Description of Fit Np Res df Res SS Res MS
1 Mod A: Ind I,Ind S 4 52 5.43 0.10
2 Mod B: Com I,Com S 2 54 39.99 0.74
3 Mod C: Ind I,Com S 3 53 6.77 0.13
4 Mod D: Com I,Ind S 3 53 20.02 0.38
ANCOVA Tests: Two Groups/Straight Line Fits
Test df SS F Stat prob
1 Ho: Equiv D.Sets 2 34.57 165.67 0e+00
2 Ho: Equiv Slopes 1 1.35 12.89 7e-04
3 Ho: Equiv Inters 1 14.59 139.88 0e+00
Call: sla.default(facxy = hellunglog)
Coefficients for Models A, B, C and D:
Model A:
Int_1 Slo_1 Int_2 Slo_2
1.63134359 -0.05319626 1.63476114 -0.05967671
Model B:
Com_Int Com_Slo
1.62731289 -0.05451464
Model C:
Int_1 Int_2 Com_Slo
1.6421324 1.6138945 -0.0553927
Model D:
Com_Int Slo_1 Slo_2
1.63251608 -0.05343178 -0.05922119
Call: sla.default(facxy = hellunglog)
Summary of ANCOVA Tests. . .
Description of Fits for 4 ANCOVA Models
Description of Fit Np Res df Res SS Res MS
1 Mod A: Ind I,Ind S 4 47 0.00 0
2 Mod B: Com I,Com S 2 49 0.01 0
3 Mod C: Ind I,Com S 3 48 0.00 0
4 Mod D: Com I,Ind S 3 48 0.00 0
ANCOVA Tests: Two Groups/Straight Line Fits
Test df SS F Stat prob
1 Ho: Equiv D.Sets 2 0.01 58.75 0.0000
2 Ho: Equiv Slopes 1 0.00 1.81 0.1853
3 Ho: Equiv Inters 1 0.00 0.02 0.8859
Call: sla.default(facxy = esdf)
Coefficients for Models A, B, C and D:
Model A:
Int_1 Slo_1 Int_2 Slo_2
-0.08734404 0.19831531 6.97037298 0.19924832
Model B:
Com_Int Com_Slo
3.4415145 0.1987818
Model C:
Int_1 Int_2 Com_Slo
-0.0992400 6.9822689 0.1987818
Model D:
Com_Int Slo_1 Slo_2
3.44151447 0.09349773 0.30406590
Call: sla.default(facxy = esdf)
Summary of ANCOVA Tests. . .
Description of Fits for 4 ANCOVA Models
Description of Fit Np Res df Res SS Res MS
1 Mod A: Ind I,Ind S 4 96 115.51 1.20
2 Mod B: Com I,Com S 2 98 1369.21 13.97
3 Mod C: Ind I,Com S 3 97 115.51 1.19
4 Mod D: Com I,Ind S 3 97 417.58 4.30
ANCOVA Tests: Two Groups/Straight Line Fits
Test df SS F Stat prob
1 Ho: Equiv D.Sets 2 1253.70 520.98 0.0000
2 Ho: Equiv Slopes 1 0.00 0.00 0.9512
3 Ho: Equiv Inters 1 302.07 251.05 0.0000
Call: sla.default(facxy = eidf)
Coefficients for Models A, B, C and D:
Model A:
Int_1 Slo_1 Int_2 Slo_2
0.03787834 0.02713860 -0.07378883 0.24299515
Model B:
Com_Int Com_Slo
-0.01795525 0.13506688
Model C:
Int_1 Int_2 Com_Slo
-2.7142926 2.6783821 0.1350669
Model D:
Com_Int Slo_1 Slo_2
-0.01795525 0.02879703 0.24133672
Call: sla.default(facxy = eidf)
Summary of ANCOVA Tests. . .
Description of Fits for 4 ANCOVA Models
Description of Fit Np Res df Res SS Res MS
1 Mod A: Ind I,Ind S 4 96 120.87 1.26
2 Mod B: Com I,Com S 2 98 1090.48 11.13
3 Mod C: Ind I,Com S 3 97 363.45 3.75
4 Mod D: Com I,Ind S 3 97 120.95 1.25
ANCOVA Tests: Two Groups/Straight Line Fits
Test df SS F Stat prob
1 Ho: Equiv D.Sets 2 969.60 385.04 0.0000
2 Ho: Equiv Slopes 1 242.58 192.66 0.0000
3 Ho: Equiv Inters 1 0.08 0.06 0.8069
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