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Age <- c(18, 23, 25, 35, 65, 54, 34, 56, 72, 19, 23, 42, 18, 39, 37)
Age
##  [1] 18 23 25 35 65 54 34 56 72 19 23 42 18 39 37
MaxHR <- c(202, 186, 187, 180, 156, 169, 174, 172, 153, 199, 193, 174, 198, 183, 178)
MaxHR
##  [1] 202 186 187 180 156 169 174 172 153 199 193 174 198 183 178
Age.MaxHR.df <- data.frame(Age = Age, MaxHeartRate = MaxHR)

Age.MaxHR.df
##    Age MaxHeartRate
## 1   18          202
## 2   23          186
## 3   25          187
## 4   35          180
## 5   65          156
## 6   54          169
## 7   34          174
## 8   56          172
## 9   72          153
## 10  19          199
## 11  23          193
## 12  42          174
## 13  18          198
## 14  39          183
## 15  37          178
lm(MaxHR ~ Age, data=Age.MaxHR.df )
## 
## Call:
## lm(formula = MaxHR ~ Age, data = Age.MaxHR.df)
## 
## Coefficients:
## (Intercept)          Age  
##    210.0485      -0.7977
summary(lm(MaxHR ~ Age, data=Age.MaxHR.df ))
## 
## Call:
## lm(formula = MaxHR ~ Age, data = Age.MaxHR.df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.9258 -2.5383  0.3879  3.1867  6.6242 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 210.04846    2.86694   73.27  < 2e-16 ***
## Age          -0.79773    0.06996  -11.40 3.85e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.578 on 13 degrees of freedom
## Multiple R-squared:  0.9091, Adjusted R-squared:  0.9021 
## F-statistic:   130 on 1 and 13 DF,  p-value: 3.848e-08
library(ggplot2)

ggplot(Age.MaxHR.df, aes(x=Age, y=MaxHeartRate)) +  geom_point(aes(color = MaxHeartRate))+theme_bw()

lm.r<- (lm(MaxHR ~ Age, data=Age.MaxHR.df ))
layout(matrix(1:4,2,2))
plot(lm.r) 

summary(lm.r)
## 
## Call:
## lm(formula = MaxHR ~ Age, data = Age.MaxHR.df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.9258 -2.5383  0.3879  3.1867  6.6242 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 210.04846    2.86694   73.27  < 2e-16 ***
## Age          -0.79773    0.06996  -11.40 3.85e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.578 on 13 degrees of freedom
## Multiple R-squared:  0.9091, Adjusted R-squared:  0.9021 
## F-statistic:   130 on 1 and 13 DF,  p-value: 3.848e-08

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