Select And Analyse Continuous Bi-Variate Data

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Mathematics - Level 3

AS90645 (3.5) Select and analyse continuous bi-variate data (Version 2)

These exemplars are based on data from two contexts.

The first involves measurements taken from a sample of mussels. Variables are the length (mm), the width (mm), the thickness (mm), the mass of the shell only (g) and the mass of the mussel without the shell (g).

The second involves data collected by a potato seed distributer from some of his clients. Variables are yield (t/ha), amount of fertiliser applied (kg/ha), average daily amount of water applied (L) over the growing season, average soil temperature (oC) over the growing season.

Student Exemplars at the Achievement boundary

Student Response (purpose statement)

I am going to use the yield and fertiliser data and my aim is to try to predict the yield of potatoes from the amount of fertiliser that is applied to the crop.

Student Response (purpose statement)

My purpose is to see if there is any relationship between the yield and the amount of fertiliser. My response variable is the yield and my explanatory variable is the amount of fertiliser.

Student Response (description of the relationship)

[pic]

There is a strong positive relationship between my two variables.

Student Response (description of the relationship)

[pic]

As the length of mussels increases the mass tends to increase. Points are close to the line of best fit and so I think it is a strong relationship.

Student Exemplars at the Merit boundary

Student Response (appropriateness)

[pic]

My model is appropriate because my r value is 0.86 which shows the relationship is strong. Also if I put a fertiliser amount of 18.5 into the regression equation I get an estimated yield of 27.6. The actual data point was 25.3 and so this means I can be confident with my model.

Student Response (appropriateness - same graph)

The r value of 0.86 is close to one and most points are close to the regression line. This means the relationship is fairly strong. However points are more scattered and above the line between 25 and 30 and are under the line for over 30. The model may not be so good for these values.

Student Response (description of R2 values)

My R2 value is 0.75. This means that 75% of the variability in yield can be explained by the variability in fertiliser.

Student Response (description of R2 values)

My R2 value is 0.75. This means that 75% of the variability in yield can be explained by the regression effect.

Student Response (causality)

There is a relationship between the length and mass of mussel but that does not mean that the length causes the mass. There might be a lurking variable that causes it.

Student Response (causality)

I found that there is a correlation between the mussel length and the mass but this does not mean that the length causes the mass. To say that the length causes the mass I would have to know more about mussels but I think it would not because both the length and mass would depend on the way the mussel grows so something that might cause the mass could be the amount of food they are given.

Student Exemplars at the Excellence boundary.

Student Response (assumptions)

When investigating the potato data I have assumed that all other variables have been constant

Student Response (assumptions)

When I got my relationship between the yield and the amount of fertiliser I had to assume that all of the other variables stayed constant. This is not so because for example the data shows that the amount of water that was applied also varies. To do it properly potatoes could be grown in the same place so that the watering and temperature would be the same.

Student Response (limitations)

I can be confident with my predictions when they are for values inside the data range because
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