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NZAMT NZQA NZ Grapher NZ Maths Census at School Study It

3.9 Bivariate HOME | Achievement Objectives | Overview | Data sets & Variable Types | Introduction | Scatter plots | Excel | iNZight | Correlation Coefficient & Linear Model | The effect of Groups & Unusual Values | Predictions | Causality | Non-Linear Models | Discussion & Conclusion | Report Writing

Predictions: Interpolation & Extrapolation

9

Making Predictions

(Achieve)
Using your (linear) model to make predictions (In context with units & rounded appropriately)

Always predict the dependent variable form a chosen explanatory variable value (Predict a 'y' from a set 'x') DISCUSS in CONTEXT

Interpolation is the prediction of values WITHIN the data range using the model.

Extrapolation is the prediction of data OUTSIDE the data range. Extrapolation should be treated with caution depending on the context and variables, and especially for non-linear models. Extrapolation should also match the nature of the data.

The precision of the prediction discussed by reviewing the strength of the relationship and the scatter on the graph close to the relevant explanatory data value.

(Merit)
Discuss the accuracy & appropriateness of the predictions
The accuracy of interpolation depends on the degree of accuracy of the models fit to the data, and what the scatter plot is like. Look at the graph and discuss in context.

 

 

Starter 5

Class notes, Class notes
Class site

McDonalds interpolation and extrapolation

Class Exemplar:
Hawai'i Island Chain: Data csv, Information page |
Google Doc write up

Class Exemplar:
American New Cars 1993
Data csv, Information pdf |
Google Doc write up

Booklet pg7, 8

Extrapolation:
Interpolation:

(Merit & Excellence)
Discussing the accuracy (precision) of the prediction (look at the level of scatter from the trend line)
Discuss relationship or causality with tespect to predictions.
Discuss appropriateness of the model.
Contextual interpretation of the gradient of the line of best fit.

(Excellence comment)
The difference in precision is probably due to the difference in gender. The shorter athletes are probably all be women so there is a strong association between height and weight. The athletes in the 185cm height range will include men and women, causing the greater range of weights (and a greater range of sports) resting in the lack of precision in the 80kg prediction. Further analysis involving the separation of the gender groups will test this hypothesis...)

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McDonalds Example: Predictions

Interpolation

The model predicts energy content (kj) = 64.4 x fat content (g) + 545kj

A product wth fat content of 23g would have a energy content of...

64.4 x 23 + 545 = 2026kj

This would be a reasonably accurate prediction as the scatter from the trend line is not significant.

The model predicts energy content (kj) = 28.9 x carbohydrate content (g) + 512kj

A product wth carbohydrate content of 25g would have a energy content of...

28.9 x 25 + 512 = 1234kj

This would be a reasonably accurate prediction as the scatter from the trend line is not significant. However predicting a value for 50g of carbohydrate would not be as accurate as the scatter from the trend line is significant.

Extrapolation

Obviously extrapolating downwards below 0g of fat is not applicable or appropriate.

 

 

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