Assignment Sample Solutions and Codes

Assighment
Sample Solutions and Codes
3/26/2020
#Exercise 3.29# data<-read.csv(file.choose(),header=T) data x<-data Calciumy ←data
ProteinProp model<-lm( y~ poly(x, degree=3)) model plot(x,y)
plot(x,y,col=‘deepskyblue4’,xlab=‘Calcium’, ylab=‘ProteinProp’,main=‘ProteinProp against
Calcium’) xsq<-xx xcub<-xx*x fit2<-lm(yx+xsq) fit3<-lm(yx+xsq+xcub) xv<-
seq(min(x),max(x),0.01) yv<-predict(fit3,list(x=xv,xsq=xv2,xcub=xv3)) lines(xv,yv,col=“black”)
summary(model)
#Question 3.29# data<-read.csv(file.choose(),header=T) x<-dataElevationy ←dataTime z<-
data$Length plot(x,y,col=‘deepskyblue4’,xlab=‘Elevation (in feet)’,ylab=‘Time (in
hours)’,main=‘Time against Elevation’) cor(x,y) model<-lm(yx+z) summary(model) summary(lm(yx))
summary(lm(yz)) r1<-lm(yz) r2<-lm(x~z) plot(r1 $residuals,r2 $residuals,main=“r2 $residuals
versus r1residuals”) lm(r1 $residuals,r2 $residuals) r3 summary(r3)
#Exercise 5.32# data<-read.csv(file.choose(),header=T) summary(data) y<-data
Birt h Weig htOzx ←dataRaceMom x1<-data$MomRace hist(y) aov(yx,data=data) aov(yx1,data=data)
reg<-lm(y~x1) anova(reg) #EXERCISE 6.25# data<-read.csv(file.choose(),header=T)
model<-aov( Ht4~Acid+Row,data=data) summary(model) model1<-
aov( Ht4~Acid+Row+AcidRow,data=data) summary(model1) model2<-
aov( Ht4~RowAcid,data=data) summary(model2)
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[Workspace loaded from ~/.RData]

> data<-read.csv(file.choose(),header=T)
> data
Calcium ProteinProp
1 -10.145390 0.1451642
2 -9.977984 0.2237115
3 -9.351250 0.2198288
4 -9.101001 0.3342694
5 -9.013766 0.3785262
6 -8.940437 0.4093691
7 -8.578232 0.5074450
8 -8.370183 0.5716413
9 -8.289037 0.6421870
10 -7.959793 0.8072800
11 -7.592269 0.9300252
12 -7.238448 0.9014096
13 -7.038626 0.9503276
14 -6.330776 0.9573205
15 -6.167236 0.9851045
16 -5.556894 0.9694070
17 -5.321209 0.9992852
18 -4.813609 1.0000000
19 -10.145390 0.1882841
20 -9.977984 0.2268408
21 -9.351250 0.2998251
22 -9.101001 0.3517163
23 -9.013766 0.4139161
24 -8.940437 0.4374755
25 -8.578232 0.5263771
26 -8.370183 0.6197400
27 -8.289037 0.6709965
28 -7.959793 0.8444435
29 -7.592269 0.9298122
30 -7.238448 0.9798032
31 -7.038626 0.9742129
32 -6.330776 0.9742309
33 -6.167236 0.9875247
34 -5.556894 0.9982300
35 -5.321209 1.0000000
36 -4.813609 0.9957145
37 -10.721933 0.2647664
38 -10.445753 0.3369681
39 -9.689732 0.4011040
40 -9.047837 0.3971727
41 -8.791559 0.5356422
42 -8.448916 0.6486877
43 -8.088203 0.6680274
44 -7.851397 0.8055475
45 -7.658565 0.8586845
46 -7.482276 0.8798047
47 -7.306449 1.0000000
48 -7.115545 0.9771862
49 -6.884057 0.9651696
50 -6.539854 0.9645220
51 -5.865186 0.9858963

> x<-data$Calcium
> y<-data$ProteinProp
> model<-lm( y~ poly(x, degree=3))
> model
Call:
lm(formula = y ~ poly(x, degree = 3))
Coefficients:
(Intercept) poly(x, degree = 3)1 poly(x, degree = 3)2 poly(x, degree = 3)3
0.6871 1.8962 -0.4988 -0.4673
> plot(x,y)
> plot(x,y,col='deepskyblue4',xlab='Calcium', ylab='ProteinProp',main='ProteinProp
against Calcium ')
> xsq<-x*x
> xcub<-x*x*x
> fit2<-lm(y~x+xsq)
> fit3<-lm(y~x+xsq+xcub)
> xv<-seq(min(x),max(x),0.01)
> yv<-predict(fit3,list(x=xv,xsq=xv^2,xcub=xv^3))
> lines(xv,yv,col="black")
> lines(x,col='green',lwd=3)
> lines(model,lwd=3,col='purple')
Error in xy.coords(x, y) :
'x' is a list, but does not have components 'x' and 'y'
> lines(y,col='purple',lwd=3)
> lines(x,y,predict(model),col='red')
Error in plot.xy(xy.coords(x, y), type = type, ...) : invalid plot type
> summary(model)
Call:
lm(formula = y ~ poly(x, degree = 3))
Residuals:
Min 1Q Median 3Q Max
-0.14031 -0.05528 -0.01859 0.05267 0.13583
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.68707 0.00994 69.120 < 2e-16 ***
poly(x, degree = 3)1 1.89623 0.07099 26.712 < 2e-16 ***
poly(x, degree = 3)2 -0.49882 0.07099 -7.027 7.44e-09 ***
poly(x, degree = 3)3 -0.46729 0.07099 -6.583 3.51e-08 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.07099 on 47 degrees of freedom
Multiple R-squared: 0.9449, Adjusted R-squared: 0.9414
F-statistic: 268.8 on 3 and 47 DF, p-value: < 2.2e-16
> plot(x,y,col='deepskyblue4',xlab='Calcium', ylab='ProteinProp',main='ProteinProp against
Calcium ')
> xv<-seq(min(x),max(x),0.01)
> yv<-predict(fit3,list(x=xv,xsq=xv^2,xcub=xv^3))

> lines(xv,yv,col="black")
> data<-read.csv(file.choose(),header=T)
> r1<-lm(y~z)
Error in eval(predvars, data, env) : object 'z' not found
> r2<-lm(x~z)
Error in eval(predvars, data, env) : object 'z' not found
> plot(r1$residuals,r2$residuals)
Error in plot(r1$residuals, r2$residuals) : object 'r1' not found
> x<-data$Elevation
> y<-data$Time
> z<-data$Length
> plot(x,y,col='deepskyblue4',xlab='Elevation (in feet)',ylab='Time (in hours)',main='Time
against Elevation')
> cor(x,y)
[1] -0.0162768
> model<-lm(y~x+z)
> summary(model)
Call:
lm(formula = y ~ x + z)
Residuals:
Min 1Q Median 3Q Max
-2.5924 -0.8050 -0.1959 0.6380 3.8432
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 8.0753787 2.5327132 3.188 0.00267 **
x -0.0014483 0.0005805 -2.495 0.01653 *
z 0.7123344 0.0593330 12.006 2.54e-15 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.37 on 43 degrees of freedom
Multiple R-squared: 0.7703, Adjusted R-squared: 0.7596
F-statistic: 72.09 on 2 and 43 DF, p-value: 1.844e-14
> summary(lm(y~x))
Call:
lm(formula = y ~ x)
Residuals:
Min 1Q Median 3Q Max
-5.6912 -1.6985 -0.5639 1.2963 7.3015
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 11.2113764 5.1953800 2.158 0.0364 *
x -0.0001269 0.0011756 -0.108 0.9145
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 2.826 on 44 degrees of freedom
Multiple R-squared: 0.0002649, Adjusted R-squared: -0.02246

F-statistic: 0.01166 on 1 and 44 DF, p-value: 0.9145
> summary(lm(y~z))
Call:
lm(formula = y ~ z)
Residuals:
Min 1Q Median 3Q Max
-2.4491 -0.6687 -0.0122 0.5590 4.0034
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.04817 0.80371 2.548 0.0144 *
z 0.68427 0.06162 11.105 2.39e-14 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.449 on 44 degrees of freedom
Multiple R-squared: 0.737, Adjusted R-squared: 0.7311
F-statistic: 123.3 on 1 and 44 DF, p-value: 2.39e-14
> r1<-lm(y~z)
> r2<-lm(x~z)
> plot(r1$residuals,r2$residuals)
> plot(r1 $residuals,r2 $residuals)
> r3<-lm(r1 $residuals,r2 $residuals)
Error in formula.default(object, env = baseenv()) : invalid formula
> summary(r3)
Error in summary(r3) : object 'r3' not found
> x<-data$Elevation
> y<-data$Time
> z<-data$Length
> plot(x,y,col='deepskyblue4',xlab='Elevation (in feet)',ylab='Time (in hours)',main='Time
against Elevation')
> cor(x,y)
[1] -0.0162768
> model<-lm(y~x+z)
> summary(model)
Call:
lm(formula = y ~ x + z)
Residuals:
Min 1Q Median 3Q Max
-2.5924 -0.8050 -0.1959 0.6380 3.8432
Coefficients:
Estimate Std. Error t value
(Intercept) 8.0753787 2.5327132 3.188
x -0.0014483 0.0005805 -2.495
z 0.7123344 0.0593330 12.006
Pr(>|t|)
(Intercept) 0.00267 **
x 0.01653 *

z 2.54e-15 ***
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1
‘ ’ 1
Residual standard error: 1.37 on 43 degrees of freedom
Multiple R-squared: 0.7703, Adjusted R-squared: 0.7596
F-statistic: 72.09 on 2 and 43 DF, p-value: 1.844e-14
> summary(lm(y~x))
Call:
lm(formula = y ~ x)
Residuals:
Min 1Q Median 3Q Max
-5.6912 -1.6985 -0.5639 1.2963 7.3015
Coefficients:
Estimate Std. Error t value
(Intercept) 11.2113764 5.1953800 2.158
x -0.0001269 0.0011756 -0.108
Pr(>|t|)
(Intercept) 0.0364 *
x 0.9145
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1
‘ ’ 1
Residual standard error: 2.826 on 44 degrees of freedom
Multiple R-squared: 0.0002649, Adjusted R-squared: -0.02246
F-statistic: 0.01166 on 1 and 44 DF, p-value: 0.9145
> summary(lm(y~z))
Call:
lm(formula = y ~ z)
Residuals:
Min 1Q Median 3Q Max
-2.4491 -0.6687 -0.0122 0.5590 4.0034
Coefficients:
Estimate Std. Error t value
(Intercept) 2.04817 0.80371 2.548
z 0.68427 0.06162 11.105
Pr(>|t|)
(Intercept) 0.0144 *
z 2.39e-14 ***
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1
‘ ’ 1

Residual standard error: 1.449 on 44 degrees of freedom
Multiple R-squared: 0.737, Adjusted R-squared: 0.7311
F-statistic: 123.3 on 1 and 44 DF, p-value: 2.39e-14
> r1<-lm(y~z)
> r2<-lm(x~z)
> plot(r1 $residuals,r2 $residuals)
> r3<-lm(r1 $residuals,r2 $residuals)
Error in formula.default(object, env = baseenv()) : invalid formula
> summary(r3)
Error in summary(r3) : object 'r3' not found
> plot(r1 $residuals,r2 $residuals)
> r3<-lm(r1 $residuals,r2 $residuals)
Error in formula.default(object, env = baseenv()) : invalid formula
> r3
Error: object 'r3' not found
> summary(r3)
Error in summary(r3) : object 'r3' not found
> r3<-lm(r1 $residuals,r2 $residuals)
Error in formula.default(object, env = baseenv()) : invalid formula
> plot(r1 $residuals,r2 $residuals,main="r2 $residuals versus r1residuals")
> lm(r1 $residuals,r2 $residuals)
Error in formula.default(object, env = baseenv()) : invalid formula
> data<read.csv(file.choose(),Header=T)
Error in read.table(file = file, header = header, sep = sep, quote = quote, :
unused argument (Header = T)
> data<read.csv(file.choose(),header=T)
Error in Ops.data.frame(data, read.csv(file.choose(), header = T)) :
‘<’ only defined for equally-sized data frames
> head
function (x, ...)
UseMethod("head")
<bytecode: 0x000001a06ca80770>
<environment: namespace:utils>
> summary(data)
Peak Elevation Difficulty Ascent Length
Algonquin Peak : 1 Min. :3820 Min. :2.000 Min. :1844 Min. : 4.80
Allen Mtn. : 1 1st Qu.:4105 1st Qu.:5.000 1st Qu.:2725 1st Qu.:10.00
Armstrong Mtn. : 1 Median :4380 Median :5.000 Median :3050 Median :12.70
Basin Mtn. : 1 Mean :4405 Mean :5.326 Mean :3096 Mean :12.57
Big Slide Mtn. : 1 3rd Qu.:4625 3rd Qu.:6.000 3rd Qu.:3490 3rd Qu.:15.20
Blake : 1 Max. :5344 Max. :7.000 Max. :4500 Max. :18.00
(Other) :40
Time
Min. : 5.00
1st Qu.: 9.00
Median :10.00
Mean :10.65
3rd Qu.:12.00
Max. :18.00
> data3<read.csv(file.choose(),header=T)
Error: object 'data3' not found
> data<read.csv(file.choose(),header=T)

Error in file.choose() : file choice cancelled
> summary(data)
Peak Elevation Difficulty Ascent Length
Algonquin Peak : 1 Min. :3820 Min. :2.000 Min. :1844 Min. : 4.80
Allen Mtn. : 1 1st Qu.:4105 1st Qu.:5.000 1st Qu.:2725 1st Qu.:10.00
Armstrong Mtn. : 1 Median :4380 Median :5.000 Median :3050 Median :12.70
Basin Mtn. : 1 Mean :4405 Mean :5.326 Mean :3096 Mean :12.57
Big Slide Mtn. : 1 3rd Qu.:4625 3rd Qu.:6.000 3rd Qu.:3490 3rd Qu.:15.20
Blake : 1 Max. :5344 Max. :7.000 Max. :4500 Max. :18.00
(Other) :40
Time
Min. : 5.00
1st Qu.: 9.00
Median :10.00
Mean :10.65
3rd Qu.:12.00
Max. :18.00
> summary(data)
Peak Elevation Difficulty Ascent Length
Algonquin Peak : 1 Min. :3820 Min. :2.000 Min. :1844 Min. : 4.80
Allen Mtn. : 1 1st Qu.:4105 1st Qu.:5.000 1st Qu.:2725 1st Qu.:10.00
Armstrong Mtn. : 1 Median :4380 Median :5.000 Median :3050 Median :12.70
Basin Mtn. : 1 Mean :4405 Mean :5.326 Mean :3096 Mean :12.57
Big Slide Mtn. : 1 3rd Qu.:4625 3rd Qu.:6.000 3rd Qu.:3490 3rd Qu.:15.20
Blake : 1 Max. :5344 Max. :7.000 Max. :4500 Max. :18.00
(Other) :40
Time
Min. : 5.00
1st Qu.: 9.00
Median :10.00
Mean :10.65
3rd Qu.:12.00
Max. :18.00
> data<read.csv(file.choose(),header=T)
Error in Ops.data.frame(data, read.csv(file.choose(), header = T)) :
‘<’ only defined for equally-sized data frames
> data<-read.csv(file.choose(),header=T)
> summary(data)
ID Plural Sex MomAge Weeks
Min. : 1.0 Min. :1.000 Min. :1.000 Min. :13.00 Min. :22.00
1st Qu.: 363.2 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:22.00 1st Qu.:38.00
Median : 725.5 Median :1.000 Median :1.000 Median :26.00 Median :39.00
Mean : 725.5 Mean :1.037 Mean :1.487 Mean :26.76 Mean :38.62
3rd Qu.:1087.8 3rd Qu.:1.000 3rd Qu.:2.000 3rd Qu.:31.00 3rd Qu.:40.00
Max. :1450.0 Max. :3.000 Max. :2.000 Max. :43.00 Max. :45.00
NA's :1
Marital RaceMom HispMom Gained Smoke BirthWeightOz
Min. :1.000 Min. :1.000 C: 2 Min. : 0.0 Min. :0.0000 Min. : 12.0
1st Qu.:1.000 1st Qu.:1.000 M: 128 1st Qu.:20.0 1st Qu.:0.0000 1st Qu.:106.0
Median :1.000 Median :1.000 N:1283 Median :30.0 Median :0.0000 Median :118.0
Mean :1.345 Mean :1.831 O: 3 Mean :30.6 Mean :0.1446 Mean :116.2
3rd Qu.:2.000 3rd Qu.:2.000 P: 9 3rd Qu.:40.0 3rd Qu.:0.0000 3rd Qu.:130.0
Max. :2.000 Max. :8.000 S: 25 Max. :95.0 Max. :1.0000 Max. :181.0

NA's :40 NA's :5
BirthWeightGm Low Premie MomRace
Min. : 340.2 Min. :0.00000 Min. :0.0000 black :332
1st Qu.:3005.1 1st Qu.:0.00000 1st Qu.:0.0000 hispanic:164
Median :3345.3 Median :0.00000 Median :0.0000 other : 48
Mean :3295.6 Mean :0.08621 Mean :0.1317 white :906
3rd Qu.:3685.5 3rd Qu.:0.00000 3rd Qu.:0.0000
Max. :5131.4 Max. :1.00000 Max. :1.0000
> y<-data$BirthWeightOz
> hist(y)
> y<-data$BirthWeightOz
> x<-RaceMom
Error: object 'RaceMom' not found
> x1<-MomRace
Error: object 'MomRace' not found
> hist(y)
> aov(y~x,data=data)
Error in model.frame.default(formula = y ~ x, data = data, drop.unused.levels = TRUE) :
variable lengths differ (found for 'x')
> summary(data)
ID Plural Sex MomAge Weeks
Min. : 1.0 Min. :1.000 Min. :1.000 Min. :13.00 Min. :22.00
1st Qu.: 363.2 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:22.00 1st Qu.:38.00
Median : 725.5 Median :1.000 Median :1.000 Median :26.00 Median :39.00
Mean : 725.5 Mean :1.037 Mean :1.487 Mean :26.76 Mean :38.62
3rd Qu.:1087.8 3rd Qu.:1.000 3rd Qu.:2.000 3rd Qu.:31.00 3rd Qu.:40.00
Max. :1450.0 Max. :3.000 Max. :2.000 Max. :43.00 Max. :45.00
NA's :1
Marital RaceMom HispMom Gained Smoke BirthWeightOz
Min. :1.000 Min. :1.000 C: 2 Min. : 0.0 Min. :0.0000 Min. : 12.0
1st Qu.:1.000 1st Qu.:1.000 M: 128 1st Qu.:20.0 1st Qu.:0.0000 1st Qu.:106.0
Median :1.000 Median :1.000 N:1283 Median :30.0 Median :0.0000 Median :118.0
Mean :1.345 Mean :1.831 O: 3 Mean :30.6 Mean :0.1446 Mean :116.2
3rd Qu.:2.000 3rd Qu.:2.000 P: 9 3rd Qu.:40.0 3rd Qu.:0.0000 3rd Qu.:130.0
Max. :2.000 Max. :8.000 S: 25 Max. :95.0 Max. :1.0000 Max. :181.0
NA's :40 NA's :5
BirthWeightGm Low Premie MomRace
Min. : 340.2 Min. :0.00000 Min. :0.0000 black :332
1st Qu.:3005.1 1st Qu.:0.00000 1st Qu.:0.0000 hispanic:164
Median :3345.3 Median :0.00000 Median :0.0000 other : 48
Mean :3295.6 Mean :0.08621 Mean :0.1317 white :906
3rd Qu.:3685.5 3rd Qu.:0.00000 3rd Qu.:0.0000
Max. :5131.4 Max. :1.00000 Max. :1.0000
> y<-data$BirthWeightOz
> x<-data$RaceMom
> x1<-data$MomRace
> hist(y)
> aov(y~x,data=data)
Call:
aov(formula = y ~ x, data = data)
Terms:
x Residuals

Sum of Squares 0.8 722333.3
Deg. of Freedom 1 1448
Residual standard error: 22.33493
Estimated effects may be unbalanced
> aov(y~x1,data=data)
Call:
aov(formula = y ~ x1, data = data)
Terms:
x1 Residuals
Sum of Squares 14002.4 708331.7
Deg. of Freedom 3 1446
Residual standard error: 22.13269
Estimated effects may be unbalanced
> reg<-lm(y~x1)
> anova(reg)
Analysis of Variance Table
Response: y
Df Sum Sq Mean Sq F value Pr(>F)
x1 3 14002 4667.5 9.5282 3.118e-06 ***
Residuals 1446 708332 489.9
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> data<-read.csv(file.choose(),header=T)
> summary(data)
Ht4 Acid Row
Min. :0.45 1.5HCl:5 a:3
1st Qu.:1.05 3.0HCl:5 b:3
Median :1.45 water :5 c:3
Mean :1.74 d:3
3rd Qu.:2.13 e:3
Max. :4.85
> mean(row,Ht4)
[1] NA
Warning message:
In mean.default(row, Ht4) :
argument is not numeric or logical: returning NA
> head(data)
Ht4 Acid Row
1 1.45 water a
2 2.79 water b
3 1.93 water c
4 2.33 water d
5 4.85 water e
6 1.00 1.5HCl a
> model<-aov( Ht4~Acid+Row,data=data)
> summary(model)
Df Sum Sq Mean Sq F value Pr(>F)
Acid 2 6.852 3.426 4.513 0.0487
Row 4 4.183 1.046 1.378 0.3235
Residuals 8 6.072 0.759

Acid *
Row
Residuals
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1
‘ ’ 1
> Ht4~Acid+Row+Acid:Row,data=data)
Error: unexpected ',' in "Ht4~Acid+Row+Acid:Row,"
> summary(model1)
Error in summary(model1) : object 'model1' not found
> model1<-aov( Ht4~Acid+Row+Acid*Row,data=data)
> summary(model1)
Df Sum Sq Mean Sq
Acid 2 6.852 3.426
Row 4 4.183 1.046
Acid:Row 8 6.072 0.759
> model1<-aov( Ht4~Acid+Row+Acid*Row,data=data)
> summary(model1)
Df Sum Sq Mean Sq
Acid 2 6.852 3.426
Row 4 4.183 1.046
Acid:Row 8 6.072 0.759
> model<-aov( Ht4~Acid+Row,data=data)
> summary(model)
Df Sum Sq Mean Sq F value Pr(>F)
Acid 2 6.852 3.426 4.513 0.0487 *
Row 4 4.183 1.046 1.378 0.3235
Residuals 8 6.072 0.759
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> model1<-aov( Ht4~Acid+Row+Acid*Row,data=data)
> summary(model1)
Df Sum Sq Mean Sq
Acid 2 6.852 3.426
Row 4 4.183 1.046
Acid:Row 8 6.072 0.759
> model2<-aov( Ht4~Row*Acid,data=data)
> summary(model2)
Df Sum Sq Mean Sq
Row 4 4.183 1.046
Acid 2 6.852 3.426
Row:Acid 8 6.072 0.759
> model2<-aov( Ht4~Row*Acid)
Error in eval(predvars, data, env) : object 'Ht4' not found
> summary(model2)
Df Sum Sq Mean Sq
Row 4 4.183 1.046
Acid 2 6.852 3.426
Row:Acid 8 6.072 0.759
> data<-read.csv(file.choose(),header=T)
> data
Calcium ProteinProp
1 -10.145390 0.1451642
2 -9.977984 0.2237115

3 -9.351250 0.2198288
4 -9.101001 0.3342694
5 -9.013766 0.3785262
6 -8.940437 0.4093691
7 -8.578232 0.5074450
8 -8.370183 0.5716413
9 -8.289037 0.6421870
10 -7.959793 0.8072800
11 -7.592269 0.9300252
12 -7.238448 0.9014096
13 -7.038626 0.9503276
14 -6.330776 0.9573205
15 -6.167236 0.9851045
16 -5.556894 0.9694070
17 -5.321209 0.9992852
18 -4.813609 1.0000000
19 -10.145390 0.1882841
20 -9.977984 0.2268408
21 -9.351250 0.2998251
22 -9.101001 0.3517163
23 -9.013766 0.4139161
24 -8.940437 0.4374755
25 -8.578232 0.5263771
26 -8.370183 0.6197400
27 -8.289037 0.6709965
28 -7.959793 0.8444435
29 -7.592269 0.9298122
30 -7.238448 0.9798032
31 -7.038626 0.9742129
32 -6.330776 0.9742309
33 -6.167236 0.9875247
34 -5.556894 0.9982300
35 -5.321209 1.0000000
36 -4.813609 0.9957145
37 -10.721933 0.2647664
38 -10.445753 0.3369681
39 -9.689732 0.4011040
40 -9.047837 0.3971727
41 -8.791559 0.5356422
42 -8.448916 0.6486877
43 -8.088203 0.6680274
44 -7.851397 0.8055475
45 -7.658565 0.8586845
46 -7.482276 0.8798047
47 -7.306449 1.0000000
48 -7.115545 0.9771862
49 -6.884057 0.9651696
50 -6.539854 0.9645220
51 -5.865186 0.9858963
> x<-data$Calcium
> y<-data$ProteinProp
> model<-lm( y~ poly(x, degree=3))
> model
Call:

lm(formula = y ~ poly(x, degree = 3))
Coefficients:
(Intercept) poly(x, degree = 3)1 poly(x, degree = 3)2 poly(x, degree = 3)3
0.6871 1.8962 -0.4988 -0.4673
> plot(x,y)
> plot(x,y,col='deepskyblue4',xlab='Calcium', ylab='ProteinProp',main='ProteinProp
against Calcium ')
> xsq<-x*x
> xcub<-x*x*x
> fit2<-lm(y~x+xsq)
> fit3<-lm(y~x+xsq+xcub)
> xv<-seq(min(x),max(x),0.01)
> yv<-predict(fit3,list(x=xv,xsq=xv^2,xcub=xv^3))
> lines(xv,yv,col="black")
> summary(model)
Call:
lm(formula = y ~ poly(x, degree = 3))
Residuals:
Min 1Q Median 3Q Max
-0.14031 -0.05528 -0.01859 0.05267 0.13583
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.68707 0.00994 69.120 < 2e-16 ***
poly(x, degree = 3)1 1.89623 0.07099 26.712 < 2e-16 ***
poly(x, degree = 3)2 -0.49882 0.07099 -7.027 7.44e-09 ***
poly(x, degree = 3)3 -0.46729 0.07099 -6.583 3.51e-08 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.07099 on 47 degrees of freedom
Multiple R-squared: 0.9449, Adjusted R-squared: 0.9414
F-statistic: 268.8 on 3 and 47 DF, p-value: < 2.2e-16
> data<-read.csv(file.choose(),header=T)
> x<-data$Elevation
> y<-data$Time
> z<-data$Length
> plot(x,y,col='deepskyblue4',xlab='Elevation (in feet)',ylab='Time (in hours)',main='Time
against Elevation')
> cor(x,y)
[1] -0.0162768
> model<-lm(y~x+z)
> summary(model)
Call:
lm(formula = y ~ x + z)
Residuals:
Min 1Q Median 3Q Max
-2.5924 -0.8050 -0.1959 0.6380 3.8432

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 8.0753787 2.5327132 3.188 0.00267 **
x -0.0014483 0.0005805 -2.495 0.01653 *
z 0.7123344 0.0593330 12.006 2.54e-15 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.37 on 43 degrees of freedom
Multiple R-squared: 0.7703, Adjusted R-squared: 0.7596
F-statistic: 72.09 on 2 and 43 DF, p-value: 1.844e-14
> summary(lm(y~x))
Call:
lm(formula = y ~ x)
Residuals:
Min 1Q Median 3Q Max
-5.6912 -1.6985 -0.5639 1.2963 7.3015
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 11.2113764 5.1953800 2.158 0.0364 *
x -0.0001269 0.0011756 -0.108 0.9145
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 2.826 on 44 degrees of freedom
Multiple R-squared: 0.0002649, Adjusted R-squared: -0.02246
F-statistic: 0.01166 on 1 and 44 DF, p-value: 0.9145
> summary(lm(y~z))
Call:
lm(formula = y ~ z)
Residuals:
Min 1Q Median 3Q Max
-2.4491 -0.6687 -0.0122 0.5590 4.0034
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.04817 0.80371 2.548 0.0144 *
z 0.68427 0.06162 11.105 2.39e-14 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.449 on 44 degrees of freedom
Multiple R-squared: 0.737, Adjusted R-squared: 0.7311
F-statistic: 123.3 on 1 and 44 DF, p-value: 2.39e-14
> r1<-lm(y~z)
> r2<-lm(x~z)

> plot(r1 $residuals,r2 $residuals,main="r2 $residuals versus r1residuals")
> lm(r1 $residuals,r2 $residuals)
Error in formula.default(object, env = baseenv()) : invalid formula
> r3
Error: object 'r3' not found
> summary(r3)
Error in summary(r3) : object 'r3' not found
> data<-read.csv(file.choose(),header=T)
> summary(data)
ID Plural Sex MomAge Weeks
Min. : 1.0 Min. :1.000 Min. :1.000 Min. :13.00 Min. :22.00
1st Qu.: 363.2 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:22.00 1st Qu.:38.00
Median : 725.5 Median :1.000 Median :1.000 Median :26.00 Median :39.00
Mean : 725.5 Mean :1.037 Mean :1.487 Mean :26.76 Mean :38.62
3rd Qu.:1087.8 3rd Qu.:1.000 3rd Qu.:2.000 3rd Qu.:31.00 3rd Qu.:40.00
Max. :1450.0 Max. :3.000 Max. :2.000 Max. :43.00 Max. :45.00
NA's :1
Marital RaceMom HispMom Gained Smoke BirthWeightOz
Min. :1.000 Min. :1.000 C: 2 Min. : 0.0 Min. :0.0000 Min. : 12.0
1st Qu.:1.000 1st Qu.:1.000 M: 128 1st Qu.:20.0 1st Qu.:0.0000 1st Qu.:106.0
Median :1.000 Median :1.000 N:1283 Median :30.0 Median :0.0000 Median :118.0
Mean :1.345 Mean :1.831 O: 3 Mean :30.6 Mean :0.1446 Mean :116.2
3rd Qu.:2.000 3rd Qu.:2.000 P: 9 3rd Qu.:40.0 3rd Qu.:0.0000 3rd Qu.:130.0
Max. :2.000 Max. :8.000 S: 25 Max. :95.0 Max. :1.0000 Max. :181.0
NA's :40 NA's :5
BirthWeightGm Low Premie MomRace
Min. : 340.2 Min. :0.00000 Min. :0.0000 black :332
1st Qu.:3005.1 1st Qu.:0.00000 1st Qu.:0.0000 hispanic:164
Median :3345.3 Median :0.00000 Median :0.0000 other : 48
Mean :3295.6 Mean :0.08621 Mean :0.1317 white :906
3rd Qu.:3685.5 3rd Qu.:0.00000 3rd Qu.:0.0000
Max. :5131.4 Max. :1.00000 Max. :1.0000
> y<-data$BirthWeightOz
> x<-data$RaceMom
> x1<-data$MomRace
> hist(y)
> aov(y~x,data=data)
Call:
aov(formula = y ~ x, data = data)
Terms:
x Residuals
Sum of Squares 0.8 722333.3
Deg. of Freedom 1 1448
Residual standard error: 22.33493
Estimated effects may be unbalanced
> aov(y~x1,data=data)
Call:
aov(formula = y ~ x1, data = data)
Terms:
x1 Residuals
Sum of Squares 14002.4 708331.7

Deg. of Freedom 3 1446
Residual standard error: 22.13269
Estimated effects may be unbalanced
> reg<-lm(y~x1)
> anova(reg)
Analysis of Variance Table
Response: y
Df Sum Sq Mean Sq F value Pr(>F)
x1 3 14002 4667.5 9.5282 3.118e-06 ***
Residuals 1446 708332 489.9
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> data<-read.csv(file.choose(),header=T)
> model<-aov( Ht4~Acid+Row,data=data)
> summary(model)
Df Sum Sq Mean Sq F value Pr(>F)
Acid 2 6.852 3.426 4.513 0.0487 *
Row 4 4.183 1.046 1.378 0.3235
Residuals 8 6.072 0.759
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> model1<-aov( Ht4~Acid+Row+Acid*Row,data=data)
> summary(model1)
Df Sum Sq Mean Sq
Acid 2 6.852 3.426
Row 4 4.183 1.046
Acid:Row 8 6.072 0.759
> model2<-aov( Ht4~Row*Acid,data=data)
> summary(model2)
Df Sum Sq Mean Sq
Row 4 4.183 1.046
Acid 2 6.852 3.426
Row:Acid 8 6.072 0.759