Lendo os dados - Turma A:

setwd("C:/Users/UFMT/Desktop")
DadosA <- read.table("Dados Turma A.csv", sep = ";", header = T, dec = ",")
rownames(DadosA) <- DadosA[,1]
DadosA <- DadosA[,-1]
attach(DadosA)
DadosA
##              Y X1 X2
## Gabriela    15  8 16
## Dalila      20  6 12
## Gustavo     20 15 30
## Leticia     40 20 40
## Luiz Ovidio 50 25 50
## Leonor      25 11 22
## Ana         10  5 10
## Antonio     55 32 64
## Julia       35 28 56
## Mariana     30 20 40

Declarando as variáveis - Turma A:

Y=as.numeric(Y)
X1=as.numeric(X1)
X2=as.numeric(X2)

Ajuste - Turma A:

ajusteA <- lm(Y~(X1+X2),data=DadosA)
resumoA <- summary(ajusteA)
resumoA
## 
## Call:
## lm(formula = Y ~ (X1 + X2), data = DadosA)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.6081  -3.9358   0.6419   5.1351   8.6486 
## 
## Coefficients: (1 not defined because of singularities)
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   5.8784     4.5323   1.297 0.230788    
## X1            1.4189     0.2355   6.025 0.000314 ***
## X2                NA         NA      NA       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.719 on 8 degrees of freedom
## Multiple R-squared:  0.8194, Adjusted R-squared:  0.7969 
## F-statistic:  36.3 on 1 and 8 DF,  p-value: 0.0003144

Correlação entre \(X_1\) e \(X_2\) - Turma A:

plot(X1,X2,ylab="Nº de Cruzamentos",xlab="Distância Percorrida", main="Figura 1: Nº de Cruzamentos em relação a Distância Percorrida até chegar a escola.", cex = 1.5, pch = 18,cex.main = 0.95)

cor.test(X1,X2)
## 
##  Pearson's product-moment correlation
## 
## data:  X1 and X2
## t = 189812531, df = 8, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  1 1
## sample estimates:
## cor 
##   1

Regressões Auxiliares Turma A

regA <- lm(X1~X2-1)
SregA <- summary(regA)
## Warning in summary.lm(regA): essentially perfect fit: summary may be unreliable
SregA
## 
## Call:
## lm(formula = X1 ~ X2 - 1)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -2.639e-15 -1.260e-15  1.280e-17  1.429e-16  1.230e-14 
## 
## Coefficients:
##     Estimate Std. Error   t value Pr(>|t|)    
## X2 5.000e-01  3.525e-17 1.419e+16   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.29e-15 on 9 degrees of freedom
## Multiple R-squared:      1,  Adjusted R-squared:      1 
## F-statistic: 2.012e+32 on 1 and 9 DF,  p-value: < 2.2e-16

Cálculo da Tolerância - Turma A:

R2_A <- SregA$r.squared 
Tol_A <- 1 - R2_A
Tol_A
## [1] 0

Cálculo do FIV - Turma A:

FIV_A = 1/Tol_A
FIV_A
## [1] Inf

Lendo os dados - Turma B:

rm(list=ls(all=TRUE)) # removendo algoritmos anteriores
DadosB <- read.table("Dados Turma B.csv", sep = ";", header = T, dec = ",")
rownames(DadosB) <- DadosB[,1]
DadosB <- DadosB[,-1]
attach(DadosB)
DadosB
##             YB X1B X2B
## Giulia      16   8  16
## Luiz Felipe 12   6  12
## Antonieta   30  15  30
## Americo     39  20  39
## Ferruccio   50  25  50
## Filomena    22  11  22
## Camilo      10   5  10
## Guilherme   64  32  64
## Maria Paula 56  28  56
## Mateus      40  20  35

Declarando as variáveis - Turma B:

YB=as.numeric(YB)
X1B=as.numeric(X1B)
X2B=as.numeric(X2B)

Ajuste - Turma B:

ajusteB <- lm(YB~(X1B+X2B),data=DadosB)
resumoB <- summary(ajusteB)
resumoB
## 
## Call:
## lm(formula = YB ~ (X1B + X2B), data = DadosB)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.88388  0.05572  0.07750  0.12524  0.17678 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -0.03395    0.24030  -0.141    0.892    
## X1B          1.96632    0.15035  13.078 3.56e-06 ***
## X2B          0.01517    0.07576   0.200    0.847    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3553 on 7 degrees of freedom
## Multiple R-squared:  0.9997, Adjusted R-squared:  0.9996 
## F-statistic: 1.285e+04 on 2 and 7 DF,  p-value: 3.336e-13

Correlação entre \(X_1\) e \(X_2\) - Turma B:

plot(X1B,X2B,ylab="Nº de Cruzamentos",xlab="Distância Percorrida", main="Figura 2: Nº de Cruzamentos em relação a Distância Percorrida até chegar a escola.", cex = 1.5, pch = 20,cex.main = 0.95)

cor.test(X1B,X2B)
## 
##  Pearson's product-moment correlation
## 
## data:  X1B and X2B
## t = 34.027, df = 8, p-value = 6.079e-10
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.9849659 0.9992179
## sample estimates:
##       cor 
## 0.9965631

Regressões Auxiliares Turma B

regB <- lm(X1B~X2B-1)
SregB <- summary(regB)
SregB
## 
## Call:
## lm(formula = X1B ~ X2B - 1)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.47681 -0.33526 -0.14155 -0.07823  2.23924 
## 
## Coefficients:
##     Estimate Std. Error t value Pr(>|t|)    
## X2B 0.507450   0.006642    76.4 5.71e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.796 on 9 degrees of freedom
## Multiple R-squared:  0.9985, Adjusted R-squared:  0.9983 
## F-statistic:  5837 on 1 and 9 DF,  p-value: 5.707e-14

Cálculo da Tolerância - Turma B:

R2_B <- SregB$r.squared 
Tol_B <- 1 - R2_B
Tol_B
## [1] 0.00153964

Cálculo do FIV - Turma B:

FIV_B = 1/Tol_B
FIV_B
## [1] 649.5024

Lendo os dados - Turma C:

rm(list=ls(all=TRUE)) # removendo algoritmos anteriores
DadosC <- read.table("Dados Turma C.csv", sep = ";", header = T, dec = ",")
rownames(DadosC) <- DadosC[,1]
DadosC <- DadosC[,-1]
attach(DadosC)
DadosC
##          YC X1C X2C
## Juliana  15   8  12
## Raquel   20   6  20
## Larissa  20  15  25
## Rogerio  40  20  37
## Isabel   50  25  32
## Wilson   25  11  17
## Luciana  10   5   9
## Sandra   55  32  60
## Oswaldo  35  28  12
## Lucas    30  20  17

Declarando as variáveis - Turma B:

YC=as.numeric(YC)
X1C=as.numeric(X1C)
X2C=as.numeric(X2C)

Ajuste - Turma B:

ajusteC <- lm(YC~(X1C+X2C),data=DadosC)
resumoC <- summary(ajusteC)
resumoC
## 
## Call:
## lm(formula = YC ~ (X1C + X2C), data = DadosC)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.2584 -2.0734 -0.9101  2.7025  8.8563 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   3.6635     3.6942   0.992  0.35439   
## X1C           1.0343     0.2448   4.224  0.00392 **
## X2C           0.3632     0.1504   2.415  0.04643 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.305 on 7 degrees of freedom
## Multiple R-squared:  0.9015, Adjusted R-squared:  0.8734 
## F-statistic: 32.03 on 2 and 7 DF,  p-value: 3e-04

Correlação entre \(X_1\) e \(X_2\) - Turma C:

plot(X1C,X2C,ylab="Nº de Cruzamentos",xlab="Distância Percorrida", main="Figura 3: Nº de Cruzamentos em relação a Distância Percorrida até chegar a escola.", cex = 1.5, pch = 17,cex.main = 0.95)

cor.test(X1C,X2C)
## 
##  Pearson's product-moment correlation
## 
## data:  X1C and X2C
## t = 2.4228, df = 8, p-value = 0.04167
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.03543846 0.90818163
## sample estimates:
##       cor 
## 0.6505491

Regressões Auxiliares Turma C

regC <- lm(X1C~X2C-1)
SregC <- summary(regC)
SregC
## 
## Call:
## lm(formula = X1C ~ X2C - 1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.4520 -2.4280 -0.0746  3.9398 20.5288 
## 
## Coefficients:
##     Estimate Std. Error t value Pr(>|t|)    
## X2C  0.62260    0.09274   6.713 8.72e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.277 on 9 degrees of freedom
## Multiple R-squared:  0.8335, Adjusted R-squared:  0.8151 
## F-statistic: 45.07 on 1 and 9 DF,  p-value: 8.719e-05

Cálculo da Tolerância - Turma C:

R2_C <- SregC$r.squared 
Tol_C <- 1 - R2_C
Tol_C
## [1] 0.1664504

Cálculo do FIV - Turma C:

FIV_C = 1/Tol_C
FIV_C
## [1] 6.007796