Predicting the size of the Terror Bird form Dinosaur data

Dinosaur data

Femur circumference	Weight(kg)	Volume
10.3	55	1092.727
13.6	115	2515.456
20.1	311	8120.601
26.7	640	19034.163
34.8	1230	42144.192
40.0	1818	64000.000
50.4	3300	128024.064
51.2	3500	134217.728
53.4	4000	152273.304

Scatter plot showing a curve trend

Plot W versus \(l^3\) and obtain approximately a straight line through the origin

# linear Regression out put

## 
## Call:
## lm(formula = `Weight(kg)` ~ Volume - 1)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -75.09 -14.37  48.69 118.96 138.20 
## 
## Coefficients:
##         Estimate Std. Error t value Pr(>|t|)    
## Volume 0.0263629  0.0003704   71.18 1.69e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 93.62 on 8 degrees of freedom
## Multiple R-squared:  0.9984, Adjusted R-squared:  0.9982 
## F-statistic:  5067 on 1 and 8 DF,  p-value: 1.69e-12

	x
Volume	0.0263629

Hence our model will be \(W=0.0263629*V\) where W represent weight and V represent volume

The model’s residuals shows some trends, so we might conclude that more work can be done in modeling. If we accept the model, having the circumference of the femur of terror bird ,we can precict that it has weight of 244.1468 kg.