To find out if there is a correlation between height and foot length using Fathom.

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Introduction

I was given some data for 60 pupils in the school, with their height, foot length and gender. Firstly, I decided to compare this data by putting this data onto a graph and see if there is a correlation between height and foot length. I think that taller people will have bigger feet, which will be my hypotheses.

Hypotheses

My hypothesis is that taller people have bigger feet.

Aim

To find out if there is a correlation between height and foot length using Fathom.

Statement

When you square root 0.69 you know to take the positive value, not the negative value, because the line has a positive gradient.

A scatter graph to show the correlation between height and foot length

The graph measures r, the strength of the linear relationship between height and the length of foot. If all the points lie very close to the line, I expect the value of r2 to be close to 1. If r2= 1 all the products lie on the straight line.

Analysis

This circle shows a few of the anomalies on the graph. The height is very big but the foot size is not. I can see this because the points are far away from the line of best fit.

The graph shows a positive correlation, which means there is a positive gradient. As the value of the y-axis increases, so does the value of the x-axis, which means that in general, as the height increases, so does the foot size. This means when I square root the value of r2, to get r, I know to take the positive square root of 0.69. For the above graph, r=0.83 to 2sf. For graphs showing positive correlation, the closer the value of r is to the line, the stronger the correlation. A positive square root and a high value of r suggests that the hypotheses I made above is correct. It then is possible to predict someone’s height if their foot length is between 15cm and 29cm.

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Now, I am going to see how this compares to three pupils in my class. The table below shows the findings. I calculated the predicted height by substituting the pupils’ foot length into the equation of the line of best fit.

I can see that Georgia and Manraj were taller than predicted when comparing their foot length and height using the above graph but Manraj was closest to the prediction. However, Jenny was shorter than predicted. As none of the predicted heights matched the actual heights, I can say that the graph does not represent the pupils ...

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