91581 Investigate Bivariate Measurement Data Assignment

Assignment Task

Introduction

Background

Research - what do your variables mean? How are they measured? How and where and by whom was the data collected? What is the background to the situation you are investigating?

Purpose

Research - about the business of the person/people/group in your purpose. Have you clearly explained that it is the relationship that you are investigating? Have you explained what someone could do with the possible results of your analysis (your model)? (e.g. this would enable person]to predict the [response variable] for the relevant value of the explanatory variable Have you referenced your sources using citations as shown in class (and in the workbook)? Variables: Have you explained how you decided which variables you would use as explanatory and response?

Hypothesis

Research-back up predictions by research for Trend, Association and Relationship type where you can

Body

For each graph: Check that your heading is sensible, check your y axis and x axis labels. Remember that a good heading includes the population. Titles should be clear and include correct units. Introduce each graph - why are you using each graph in your analysis?

State the linear regression model: Have you explained all of the features of the equation. If (for example) your y axis intercept is not at zero what does this tell you? Does it suggest a problem with the model or is it fine? If there is a problem, perhaps that helps to suggest a different model later or simply that you need to acknowledge a limitation of your model. Often worth pointing out the difference between correlation and causation, remembering that we cannot claim causation without a properly designed experiment.

Make at least two predictions: Have you rounded them sensibly and included units? Have you chosen interesting values of the explanatory variable for your prediction? For example, have you found a region where you have lots/ very little scatter so you can discuss confidence in your prediction? Have you found a region where most of the scatter is above/below the regression line.

so you can discuss over or under estimation? Have you done an extrapolation (beyond the range of the explanatory variable) so that you can talk about confidence and link later on to how a different model might be better or worse for the same extrapolation? Have you used research to find suitable points to predict (eg biggest ever, median in NZ, mean in NZ, etc)? You could also link your confidence in your prediction to the r value in a linear model (obviously higher the value the higher the confidence in general)

For each piece of analysis: Have you told us why you are doing it? Eg The low r value of the linear model suggests that there must be at least one confounding variable, so I have decided to investigate the addition of a third variable by using the "colour by" option on NZ Grapher. Have you told us how it compares your hypothesis? Have you explained how what you have learned from that piece of analysis would be useful for the people in your purpose? Note that it is only worth doing model improvements that are appropriate and applicable to the selected dataset. Also only do a predictions comparison between different models when there is a significant difference in result to show an improved model.

Conclusion

If you switched to a different model (linear without outliers, non-linear, subgrouped), tell us why you did that and make your conclusion about that new model. If you didn't switch, why not? Justification for your chosen model might include points about about accuracy of predictions (including extrapolations), visual fit to data, y intercepts, support from research as to what the model should be like, simplicity (linear is very simple for people to understand)
Tell the people in your purpose that the situation is best modelled with the model you have chosen. Make clear how this model will help them! Link back to hypothesis for what you expected to see.

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