Afreen Banu Project R
Afreen Banu
January 10, 2018
Project Title: To understand the effect of various parameters on Radius, Texture, Perimeter, Area, Smoothness, Compactness, Concavity, Symmetry, Fracal Dimension of the Breast Cancer Infection belonging to either a Molecular Level Diagnosis or Hepatitis B Diagnosis.
NAME: Afreen Banu
EMAIL: afreen.banu1995@gmail.com
COMPANY: Amazon
library(readxl)
BCData <- read_excel("C:/Users/afrebanu/Desktop/BCData.xlsx")
View(BCData)mean(BCData$radius_mean)## [1] 14.12729boxplot(BCData$radius_mean)
boxplot(BCData$radius_mean,horizontal = TRUE,main="Mean Radius of the Breast Cancer Infection")
mean(BCData$texture_mean)## [1] 19.28965boxplot(BCData$texture_mean,horizontal = TRUE,main="Mean Texture of the Breast Cancer Infection")
table(BCData$Diagnosis)##
## B M
## 357 212boxplot(BCData$radius_mean~BCData$Diagnosis,main="Radius Comparison for different types of Diagnosis")
boxplot(BCData$radius_mean~BCData$Diagnosis,main="Radius Comparison for different types of Diagnosis",xlab="Types of Diagnosis",ylab="Mean Radius of the Infection",col="orange",border="brown")
#This Proves that the mean radius of infection is much higher in terms of a Molecular Level Infection than that of Hepatitis B Infection.
{r}
boxplot(BCData$texture_mean~BCData$Diagnosis,main="Texture Comparison for different types of Diagnosis",xlab="Types of Diagnosis",ylab="Mean Texture of the Infection",col="orange",border="brown")This Proves that though the mean texture of infection is higher in terms of a Molecular Level Infection than that of Hepatitis B Infection but also there are many outliers for a Hepatitis B Infection whose value is much more than the median Texture of the Infection.
boxplot(BCData$perimeter_mean~BCData$Diagnosis,main="Perimeter Comparison for different types of Diagnosis",xlab="Types of Diagnosis",ylab="Mean Perimeter of the Infection",col="orange",border="brown")
This shos that people with B type of Diagnosis have much less Perimeter of their infection as compared to the people who have an infection at the molecular level.
boxplot(BCData$area_mean~BCData$Diagnosis,main="Area Comparison for different types of Diagnosis",xlab="Types of Diagnosis",ylab="Mean Area of the Infection",col="orange",border="brown")
This shows that people with B type of Diagnosis have much less affected area of their infection as compared to the people who have an infection at the molecular level. The maximum affected area for a B Type of Diagnosis falls somewhere around the median of the affected area of the infection in people which have a Molecular Level of diagnosis.
boxplot(BCData$compactness_mean~BCData$Diagnosis,main="Compactness Comparison for different types of Diagnosis",xlab="Types of Diagnosis",ylab="Mean Compactness of the Infection",col="orange",border="brown")
Tumor Compactness is also much high in people with Modeular Level of Diagnosis.
boxplot(BCData$symmetry_mean~BCData$Diagnosis,main="Symmetry Comparison for different types of Diagnosis",xlab="Types of Diagnosis",ylab="Mean Symmetry of the Infection",col="orange",border="brown")
There is not much different in the Median values of Symmetry of the tumor in different types of diagnosis but there are several outliers in M type of Diagnosis who have very high symmetry.
On understanding these box plots, it is evident that no doubt there are more people with B type of diagnosis, their affected area by tumor, Perimeter and Radius of Tumor and many other parameters are still lesser as compared to people who have Molecular Type of Diagnosis.
library(car)
scatterplot(BCData$radius_mean,BCData$radius_se)
scatterplot(BCData$radius_mean,BCData$radius_worst)
#There are very few negative coreealtions in the above data.
scatterplot(BCData$texture_se,BCData$texture_mean)
scatterplot(BCData$texture_worst,BCData$texture_mean)
Texture_Worst is better correlated with Texture_Mean.
library(car)
scatterplot(BCData$perimeter_worst,BCData$perimeter_mean)
scatterplot(BCData$perimeter_mean,BCData$radius_mean)
scatterplot(BCData$area_mean,BCData$radius_mean)
scatterplot(BCData$smoothness_mean,BCData$radius_mean)
scatterplot(BCData$compactness_mean,BCData$radius_mean)
scatterplot(BCData$concavity_mean,BCData$radius_mean)
scatterplot(BCData$symmetry_mean,BCData$radius_mean)
scatterplot(BCData$fractal_dimension_mean,BCData$radius_mean)
lm(formula = radius_mean~texture_mean+perimeter_mean+area_mean+smoothness_mean+compactness_mean+concavity_mean+symmetry_mean+fractal_dimension_mean,data = BCData)##
## Call:
## lm(formula = radius_mean ~ texture_mean + perimeter_mean + area_mean +
## smoothness_mean + compactness_mean + concavity_mean + symmetry_mean +
## fractal_dimension_mean, data = BCData)
##
## Coefficients:
## (Intercept) texture_mean perimeter_mean
## 0.1230069 0.0002433 0.1566960
## area_mean smoothness_mean compactness_mean
## -0.0002887 1.1235625 -4.8493119
## concavity_mean symmetry_mean fractal_dimension_mean
## -0.8203314 0.2234977 3.3052993lm(formula = radius_mean~texture_mean+perimeter_mean+area_mean+smoothness_mean+compactness_mean+concavity_mean+symmetry_mean+fractal_dimension_mean,data = BCData)##
## Call:
## lm(formula = radius_mean ~ texture_mean + perimeter_mean + area_mean +
## smoothness_mean + compactness_mean + concavity_mean + symmetry_mean +
## fractal_dimension_mean, data = BCData)
##
## Coefficients:
## (Intercept) texture_mean perimeter_mean
## 0.1230069 0.0002433 0.1566960
## area_mean smoothness_mean compactness_mean
## -0.0002887 1.1235625 -4.8493119
## concavity_mean symmetry_mean fractal_dimension_mean
## -0.8203314 0.2234977 3.3052993fit1<-lm(formula = radius_mean~texture_mean,data = BCData)
fit1##
## Call:
## lm(formula = radius_mean ~ texture_mean, data = BCData)
##
## Coefficients:
## (Intercept) texture_mean
## 9.0099 0.2653plot(fit1)
summary(fit1)##
## Call:
## lm(formula = radius_mean ~ texture_mean, data = BCData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.068 -2.195 -0.581 1.766 14.200
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.00993 0.64339 14.004 < 2e-16 ***
## texture_mean 0.26529 0.03256 8.149 2.36e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.337 on 567 degrees of freedom
## Multiple R-squared: 0.1048, Adjusted R-squared: 0.1033
## F-statistic: 66.4 on 1 and 567 DF, p-value: 2.36e-15fit2<-lm(formula = radius_mean~perimeter_mean,data = BCData)
summary(fit2)##
## Call:
## lm(formula = radius_mean ~ perimeter_mean, data = BCData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.43367 -0.10445 0.02596 0.14652 0.60550
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.8177520 0.0379227 21.56 <2e-16 ***
## perimeter_mean 0.1447176 0.0003987 362.99 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2309 on 567 degrees of freedom
## Multiple R-squared: 0.9957, Adjusted R-squared: 0.9957
## F-statistic: 1.318e+05 on 1 and 567 DF, p-value: < 2.2e-16The R-Squared value for this model is 99.57%. For now, this is the most Statistically significant model.
fit3<-lm(formula = radius_mean~area_mean,data = BCData)
summary(fit3)##
## Call:
## lm(formula = radius_mean ~ area_mean, data = BCData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.9604 -0.1801 0.1479 0.3600 0.7788
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.652e+00 4.955e-02 154.4 <2e-16 ***
## area_mean 9.887e-03 6.666e-05 148.3 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5591 on 567 degrees of freedom
## Multiple R-squared: 0.9749, Adjusted R-squared: 0.9748
## F-statistic: 2.2e+04 on 1 and 567 DF, p-value: < 2.2e-16The p-value is same for this model but R-squared value is a bit less. It still means that fit2 is statitically a better linear model then fit3.
fit4<-lm(formula = radius_mean~smoothness_mean,data = BCData)
summary(fit4)##
## Call:
## lm(formula = radius_mean ~ smoothness_mean, data = BCData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.0285 -2.3750 -0.5561 1.6571 13.2202
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.01 1.01 9.912 < 2e-16 ***
## smoothness_mean 42.74 10.37 4.122 4.31e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.475 on 567 degrees of freedom
## Multiple R-squared: 0.0291, Adjusted R-squared: 0.02739
## F-statistic: 16.99 on 1 and 567 DF, p-value: 4.313e-05fit5<-lm(formula = radius_mean~compactness_mean,data = BCData)
summary(fit5)##
## Call:
## lm(formula = radius_mean ~ compactness_mean, data = BCData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.8971 -2.0131 -0.4438 1.5317 12.3867
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.6035 0.2826 37.52 <2e-16 ***
## compactness_mean 33.7722 2.4169 13.97 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.042 on 567 degrees of freedom
## Multiple R-squared: 0.2562, Adjusted R-squared: 0.2548
## F-statistic: 195.3 on 1 and 567 DF, p-value: < 2.2e-16fit6<-lm(formula = radius_mean~concavity_mean,data = BCData)
summary(fit6)##
## Call:
## lm(formula = radius_mean ~ concavity_mean, data = BCData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.0295 -1.5416 -0.1348 1.5333 7.8383
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.471 0.163 70.36 <2e-16 ***
## concavity_mean 29.917 1.367 21.89 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.597 on 567 degrees of freedom
## Multiple R-squared: 0.458, Adjusted R-squared: 0.4571
## F-statistic: 479.1 on 1 and 567 DF, p-value: < 2.2e-16fit7<-lm(formula = radius_mean~symmetry_mean,data = BCData)
summary(fit7)##
## Call:
## lm(formula = radius_mean ~ symmetry_mean, data = BCData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.3711 -2.4426 -0.5862 1.5744 14.2934
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 10.6867 0.9783 10.924 < 2e-16 ***
## symmetry_mean 18.9918 5.3393 3.557 0.000406 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.488 on 567 degrees of freedom
## Multiple R-squared: 0.02183, Adjusted R-squared: 0.0201
## F-statistic: 12.65 on 1 and 567 DF, p-value: 0.0004065fit8<-lm(formula = radius_mean~fractal_dimension_mean,data = BCData)
summary(fit8)##
## Call:
## lm(formula = radius_mean ~ fractal_dimension_mean, data = BCData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.9829 -2.4195 -0.9257 1.7852 12.8087
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23.895 1.259 18.985 < 2e-16 ***
## fractal_dimension_mean -155.545 19.918 -7.809 2.8e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.352 on 567 degrees of freedom
## Multiple R-squared: 0.09711, Adjusted R-squared: 0.09552
## F-statistic: 60.99 on 1 and 567 DF, p-value: 2.795e-14summary(fit2)##
## Call:
## lm(formula = radius_mean ~ perimeter_mean, data = BCData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.43367 -0.10445 0.02596 0.14652 0.60550
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.8177520 0.0379227 21.56 <2e-16 ***
## perimeter_mean 0.1447176 0.0003987 362.99 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2309 on 567 degrees of freedom
## Multiple R-squared: 0.9957, Adjusted R-squared: 0.9957
## F-statistic: 1.318e+05 on 1 and 567 DF, p-value: < 2.2e-16