dat<-ToothGrowth

Independent and Dependent Variable

Independent Variable: The doses of OJ and VC consumed. Dependent Variable: The length of the odontoblast.

Linear Regression

model<- lm(len~dose,data=dat)
summary(model)
## 
## Call:
## lm(formula = len ~ dose, data = dat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.4496 -2.7406 -0.7452  2.8344 10.1139 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   7.4225     1.2601    5.89 2.06e-07 ***
## dose          9.7636     0.9525   10.25 1.23e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.601 on 58 degrees of freedom
## Multiple R-squared:  0.6443, Adjusted R-squared:  0.6382 
## F-statistic: 105.1 on 1 and 58 DF,  p-value: 1.233e-14
plot(dat$dose, dat$len, main="Scatterplot of Dose vs Len",
     xlab="Dose", ylab="Tooth Length")
abline(model, col="red")

Analysis

Since the p-value of the given data 1.233e-14 is smaller than the significance level of 0.05, we can conclude that the coefficient of the regression line is NOT 0; thus, there is a relationship between the does of VC/OG and the tooth length.

Drawing the Scatterplot

pairs(dat)

dat<-read.csv("/Users/nabinwon/Downloads/aminoAcid.csv")

Independent and Dependent Variable

Independent Variable: Doses of AminoAcid and its type Dependent Variable: The patient’s nutritional level

dat$AminoAcid<-as.factor(dat$AminoAcid)
dat$dose<-as.factor(dat$dose)
str(dat)
## 'data.frame':    18 obs. of  3 variables:
##  $ AminoAcid: Factor w/ 2 levels "lysine","methionine": 2 2 2 2 2 2 2 2 2 1 ...
##  $ dose     : Factor w/ 3 levels "10","20","30": 1 1 1 2 2 2 3 3 3 1 ...
##  $ response : num  15 16 14.5 17 19 18.5 14 13.5 14.5 30 ...
model <- lm(response ~ AminoAcid + dose, data = dat)
summary(model)
## 
## Call:
## lm(formula = response ~ AminoAcid + dose, data = dat)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.8889 -2.9861  0.0833  2.6111  5.3889 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           32.861      1.729  19.005 2.15e-11 ***
## AminoAcidmethionine  -20.222      1.729 -11.695 1.30e-08 ***
## dose20                 3.667      2.118   1.731   0.1053    
## dose30                 5.750      2.118   2.715   0.0168 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.668 on 14 degrees of freedom
## Multiple R-squared:  0.9116, Adjusted R-squared:  0.8926 
## F-statistic: 48.11 on 3 and 14 DF,  p-value: 1.275e-07

Anlaysis

Since the p-value of the given data 0.0137 and 4.20e-09 is less than the significance level of 0.05, we can conclude that the number of doses and the type of amino acid affects the patient’s nutritional level.