Introduction

This is a data set based on the heights of the female Olympic volleyball champions from the years 1956 to 2016. This data was collected from topsports.com “Anthropometric Measurements of Olympic Gymnastics Champions”

Data

#Data on the eights and weights of gymnast champions
Fheight <- c(1.61, 1.61, 1.60, 1.60, 1.60, 1.52, 1.48, 1.45, 1.47, 1.37, 1.49, 1.58, 1.52, 1.60, 1.50, 1.45)
length(Fheight)
## [1] 16
Fweight <- c(52, 52, 58, 58, 52, 39, 45, 42, 41, 32, 42, 44, 44, 45, 41, 47)

#Sequence of years 
year <- seq(1956, 2016, 4)

year
##  [1] 1956 1960 1964 1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 2008 2012
## [16] 2016
Fheight
##  [1] 1.61 1.61 1.60 1.60 1.60 1.52 1.48 1.45 1.47 1.37 1.49 1.58 1.52 1.60 1.50
## [16] 1.45
Fweight
##  [1] 52 52 58 58 52 39 45 42 41 32 42 44 44 45 41 47
#Linear regression calculations and data
BL <- lm(Fweight ~ Fheight)
summary(BL)
## 
## Call:
## lm(formula = Fweight ~ Fheight)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.2693 -2.2598 -0.2603  2.1400  6.9491 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   -68.04      23.79  -2.860 0.012596 *  
## Fheight        74.55      15.55   4.794 0.000286 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.454 on 14 degrees of freedom
## Multiple R-squared:  0.6214, Adjusted R-squared:  0.5944 
## F-statistic: 22.98 on 1 and 14 DF,  p-value: 0.000286
coef(BL)
## (Intercept)     Fheight 
##   -68.04464    74.54864
fitted <- coef(BL)
int <- fitted[1]
slope <- fitted[2]
slope
##  Fheight 
## 74.54864
#plotting height(x) and weight(y)
plot(Fheight, Fweight, main = "Heights and Weight of Female Olympic Athletes")

#library(plotrix)
abline(BL,col = "red")

# ablineclip(a =0.0, b = 0.03,x1=1,x2=18)
# ablineclip(a= 0.0, b = 0.06,x1=1,x2=18)

#Residual Info
Scon <- seq(1.37 ,1.62, 0.01625)
length(Scon)
## [1] 16
## [1] 16
rnoise <- rnorm(16,0,0.1)
length(rnoise)
## [1] 16
## [1] 16
Sabs <- 0.0435 * Scon + 0.026 + rnoise
plot(Scon,Sabs)

SBL <- lm(Sabs ~ Scon)
summary(SBL)
## 
## Call:
## lm(formula = Sabs ~ Scon)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.19847 -0.03272  0.01042  0.03759  0.13148 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)  -0.3290     0.4106  -0.801    0.436
## Scon          0.2600     0.2749   0.946    0.360
## 
## Residual standard error: 0.08236 on 14 degrees of freedom
## Multiple R-squared:  0.06007,    Adjusted R-squared:  -0.007071 
## F-statistic: 0.8947 on 1 and 14 DF,  p-value: 0.3603
plot(Scon,residuals(SBL), main = "Residual Plot")
abline(a = 0.0, b = 0.0, col = "blue")

Discussion

The p value is 0.000286.

The calculated Standard Deviation is 23.79.

The r value squared is 0.6214.

The slope is 74.56864.

The y-intercept is -68.04464.

Examining the data based on the height and weight of female Olympic athletes, there is a positive correlation, as the heights of athletes increase, their weights also increase.