Student Weight Prediction

The given dataset has height and weight of 10 students. We would like to see if weight is having a linear relationship with height and would like to establish the regression model for weight prediction using Simple Linear Regression

dim(student)

## [1] 10  2

student

##    ht  wt
## 1  63 127
## 2  64 121
## 3  66 142
## 4  69 157
## 5  69 162
## 6  71 156
## 7  71 169
## 8  72 165
## 9  73 181
## 10 75 208

attach(student)
par(mfrow =c(2,2))
boxplot(wt, horizontal = TRUE, main="Boxplot of Wt")
boxplot(ht, horizontal = TRUE, main="Boxplot of Ht")
hist(wt)
hist(ht)

par(mfrow=c(1,1))

plot(ht,wt, col="Blue", main="Height Vs Weight")

cor.test(ht,wt)

## 
##  Pearson's product-moment correlation
## 
## data:  ht and wt
## t = 8.3466, df = 8, p-value = 3.214e-05
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.7864411 0.9877259
## sample estimates:
##       cor 
## 0.9470984

The plot shows the relationship between Height and Weight. From the Pearson’s correlation test, we see that 0.9470984. Thus we see that there is high positive correlation between height and weight.

Now let us establish a regression model to predict weight:

SLM <- lm(wt~ht, data=student)
summary(SLM)

## 
## Call:
## lm(formula = wt ~ ht, data = student)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.2339  -4.0804  -0.0963   4.6445  14.2158 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -266.5344    51.0320  -5.223    8e-04 ***
## ht             6.1376     0.7353   8.347 3.21e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.641 on 8 degrees of freedom
## Multiple R-squared:  0.897,  Adjusted R-squared:  0.8841 
## F-statistic: 69.67 on 1 and 8 DF,  p-value: 3.214e-05

anova(SLM)

## Analysis of Variance Table
## 
## Response: wt
##           Df Sum Sq Mean Sq F value    Pr(>F)    
## ht         1 5202.2  5202.2  69.666 3.214e-05 ***
## Residuals  8  597.4    74.7                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

From the above regression model summary, we see can infer the following:

• The intercept b0 = -266.5344, As the p-value (3.214e-05) is less than alpha, we see that the b0 is statistically significant.
• The coefficient b1 = 6.1376. As the p-value (8e-04) is less than alpha, we see that the b1 is statistically significant.
• The coefficient of determination R-squared value is 0.897.It means that 89.7% variation in weight is reduced by taking into account height of the student.
• The residual error (s) is 8.641 lbs.

The regression plot is shown below:

plot(ht, wt, xlab="height", ylab="Weight", abline(lm(wt~ht),col=c("Blue")), main="Simple Linear Regression")