cancer <- read.csv("cancer.csv")

#Figure 1.1

n <- nrow(cancer)
Y <- cancer$Mean_Area
X <- cancer$Mean_mean_G #
min(X)
## [1] 47.49451
max(X)
## [1] 110.6758
mean(X)
## [1] 73.90454
sd(X)
## [1] 12.42109
linmod <- lm(Y ~ X)
plot(
   X,
   Y,
   xlab = "Average Green Intensity", #
   ylab = "Average nuclear area",
   pch = 16,
   col = "Green", #
)

title(main = "Figure 1.1: Green Color Intensity And Average Nuclear Area") #
b0 <- linmod$coef[1]
b1 <- linmod$coef[2]
abline(a = b0, b = b1, col = "orange")

summary(linmod)
## 
## Call:
## lm(formula = Y ~ X)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -241.42  -85.27  -15.04   65.08  642.15 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  227.423     62.867   3.618 0.000395 ***
## X              5.851      0.839   6.974 7.06e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 134.3 on 165 degrees of freedom
## Multiple R-squared:  0.2277, Adjusted R-squared:  0.223 
## F-statistic: 48.64 on 1 and 165 DF,  p-value: 7.058e-11
Y.hat <- linmod$fitted.values
SSR <- sum((Y.hat - mean(Y)) ^ 2)
SSE <- sum((Y - Y.hat) ^ 2)

MSR <- SSR / 1
MSE <- SSE / (n - 2)

F.statistic <- MSR / MSE


#Figure 1.2

n <- nrow(cancer)
Y <- cancer$Mean_Area
X <- cancer$Mean_mean_G #
min(X)
## [1] 47.49451
max(X)
## [1] 110.6758
mean(X)
## [1] 73.90454
sd(X)
## [1] 12.42109
linmod <- lm(Y ~ X)
plot(
   X,
   Y,
   xlab = "Average Green Intensity", #
   ylab = "Average nuclear area",
   pch = 16,
   col = "Green", #
)

title(main = "Figure 1.2: Blue Color Intensity And Average Nuclear Area") #
b0 <- linmod$coef[1]
b1 <- linmod$coef[2]
abline(a = b0, b = b1, col = "orange")

summary(linmod)
## 
## Call:
## lm(formula = Y ~ X)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -241.42  -85.27  -15.04   65.08  642.15 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  227.423     62.867   3.618 0.000395 ***
## X              5.851      0.839   6.974 7.06e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 134.3 on 165 degrees of freedom
## Multiple R-squared:  0.2277, Adjusted R-squared:  0.223 
## F-statistic: 48.64 on 1 and 165 DF,  p-value: 7.058e-11
Y.hat <- linmod$fitted.values
SSR <- sum((Y.hat - mean(Y)) ^ 2)
SSE <- sum((Y - Y.hat) ^ 2)

MSR <- SSR / 1
MSE <- SSE / (n - 2)

F.statistic <- MSR / MSE


#Figure 1.3


n <- nrow(cancer)
Y <- cancer$Mean_Area
X <- cancer$Mean_mean_B #
min(X)
## [1] 72.08346
max(X)
## [1] 128.9248
mean(X)
## [1] 94.72136
sd(X)
## [1] 10.84549
linmod <- lm(Y ~ X)
plot(
   X,
   Y,
   xlab = "Average Red Intensity", #
   ylab = "Average nuclear area",
   pch = 16,
   col = "Blue", #
)

title(main = "Figure 1.3: Blue Color Intensity And Average Nuclear Area") #
b0 <- linmod$coef[1]
b1 <- linmod$coef[2]
abline(a = b0, b = b1, col = "orange")

summary(linmod)
## 
## Call:
## lm(formula = Y ~ X)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -212.24  -88.20  -11.88   63.00  614.36 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -40.3952    88.6243  -0.456    0.649    
## X             7.3927     0.9296   7.953 2.75e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 129.9 on 165 degrees of freedom
## Multiple R-squared:  0.2771, Adjusted R-squared:  0.2727 
## F-statistic: 63.24 on 1 and 165 DF,  p-value: 2.748e-13
Y.hat <- linmod$fitted.values
SSR <- sum((Y.hat - mean(Y)) ^ 2)
SSE <- sum((Y - Y.hat) ^ 2)

MSR <- SSR / 1
MSE <- SSE / (n - 2)

F.statistic <- MSR / MSE


cancer <- read.csv("cancer.csv")


n <- nrow(cancer)
Y <- cancer$Mean_Area
X <- cancer$Mean_mean_B #
min(X)
## [1] 72.08346
max(X)
## [1] 128.9248
mean(X)
## [1] 94.72136
sd(X)
## [1] 10.84549
linmod <- lm(Y ~ X)
plot(
   X,
   Y,
   xlab = "Average Red Intensity", #
   ylab = "Average nuclear area",
   pch = 16,
   col = "Blue", #
)

title(main = "Figure 1.3: Blue Color Intensity And Average Nuclear Area") #
b0 <- linmod$coef[1]
b1 <- linmod$coef[2]
abline(a = b0, b = b1, col = "orange")

summary(linmod)
## 
## Call:
## lm(formula = Y ~ X)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -212.24  -88.20  -11.88   63.00  614.36 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -40.3952    88.6243  -0.456    0.649    
## X             7.3927     0.9296   7.953 2.75e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 129.9 on 165 degrees of freedom
## Multiple R-squared:  0.2771, Adjusted R-squared:  0.2727 
## F-statistic: 63.24 on 1 and 165 DF,  p-value: 2.748e-13
Y.hat <- linmod$fitted.values
SSR <- sum((Y.hat - mean(Y)) ^ 2)
SSE <- sum((Y - Y.hat) ^ 2)

MSR <- SSR / 1
MSE <- SSE / (n - 2)

F.statistic <- MSR / MSE


#Figure 1.4


n <- nrow(cancer)
Y <- cancer$Mean_Area
X <- cancer$Mean_mean_HSV #
min(X)
## [1] 64.13022
max(X)
## [1] 131.2717
mean(X)
## [1] 90.31242
sd(X)
## [1] 13.5191
linmod <- lm(Y ~ X)
plot(
   X,
   Y,
   xlab = "Average HSV Value", #
   ylab = "Average nuclear area",
   pch = 16,
   col = "Purple", #
)

title(main = "Figure 1.4: HSV And Average Nuclear Area") #
b0 <- linmod$coef[1]
b1 <- linmod$coef[2]
abline(a = b0, b = b1, col = "orange")

summary(linmod)
## 
## Call:
## lm(formula = Y ~ X)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -216.81  -76.39  -13.02   66.50  587.15 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  68.5727    65.1806   1.052    0.294    
## X             6.5471     0.7138   9.172   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 124.3 on 165 degrees of freedom
## Multiple R-squared:  0.3377, Adjusted R-squared:  0.3337 
## F-statistic: 84.12 on 1 and 165 DF,  p-value: < 2.2e-16
Y.hat <- linmod$fitted.values
SSR <- sum((Y.hat - mean(Y)) ^ 2)
SSE <- sum((Y - Y.hat) ^ 2)

MSR <- SSR / 1
MSE <- SSE / (n - 2)

F.statistic <- MSR / MSE


#Figure 1.5


n <- nrow(cancer)
Y <- cancer$Mean_Area
X <- cancer$Mean_mean_BR #
min(X)
## [1] 0
max(X)
## [1] 67.65289
mean(X)
## [1] 7.98594
sd(X)
## [1] 11.35399
linmod <- lm(Y ~ X)
plot(
   X,
   Y,
   xlab = "Average BR Value", #
   ylab = "Average nuclear area",
   pch = 16,
   col = "Purple", #
)

title(main = "Figure 1.5: BR And Average Nuclear Area") #
b0 <- linmod$coef[1]
b1 <- linmod$coef[2]
abline(a = b0, b = b1, col = "orange")

summary(linmod)
## 
## Call:
## lm(formula = Y ~ X)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -262.41  -90.99  -13.53   61.53  737.19 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  633.489     14.023  45.175  < 2e-16 ***
## X              3.302      1.012   3.262  0.00135 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 148.1 on 165 degrees of freedom
## Multiple R-squared:  0.06057,    Adjusted R-squared:  0.05488 
## F-statistic: 10.64 on 1 and 165 DF,  p-value: 0.001346
Y.hat <- linmod$fitted.values
SSR <- sum((Y.hat - mean(Y)) ^ 2)
SSE <- sum((Y - Y.hat) ^ 2)

MSR <- SSR / 1
MSE <- SSE / (n - 2)

F.statistic <- MSR / MSE