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Bivariate Data, SM-Bank 009

The height (in cm) and foot length (in cm) for each of eight Year 12 students were recorded and displayed in the scatterplot below.

A line of best fit has been fitted to the data as shown.
 

  1. Determine the predicted foot size of a student who is 176 centimetres tall.   (1 mark)
  2. Calculate the gradient of the line of best fit, giving your answer correct to two decimal places.   (2 marks)
  3. What is the equation of the line of best fit?   (2 marks)
Show Answers Only

i.    \(\text{Height 176 cm}\ \ \Rightarrow\ \ \text{Foot length = 27 cm} \)

ii.    \(1.29 \)

iii.    \(\textit{height}\ = 141.2 + 1.29 \times \textit{foot length} \)

Show Worked Solution

i.    \(\text{Height 176 cm}\ \ \Rightarrow\ \ \text{Foot length = 27 cm} \)
 

ii.    \(\text{LOBF passes through (20, 167) and (34, 185):}\)

\(\text{Gradient}\ = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{185-167}{34-20} = \dfrac{18}{14} = 1.285… = 1.29 \)
 

iii.   \(\text{Equation}\ \ \Rightarrow \ \ \text{Gradient = 1.29, passes through (20, 167)} \)

\(y-y_1 \) \(=m(x-x_1) \)  
\(y-167\) \(=1.29(x-20) \)  
\(y\) \(=1.29x + 141.2\)  

 
\(\textit{height}\ = 141.2 + 1.29 \times \textit{foot length} \)