BIVARIATE DATA 1
Please review Level 1 Bi-variate data before continuing in this section.
a couple of Guidelines for your assessment
1. For merit or excellence write an introduction showing background information with links, and your interest.
2. What other variables other than your chosen explanatory variable might influence your response variable?
3. State that your question is that you will investigate whether there is a relationship between your chosen explanatory variable and your chosen response variable.
4. State clearly what your chosen explanatory variable (x-axis) is, and what your chosen response variable is (y-axis). Give the units.
5. For merit or excellence, state why you have chosen your explanatory variable and response variable, and how you think your explanatory variable will affect your response variable.
2. What other variables other than your chosen explanatory variable might influence your response variable?
3. State that your question is that you will investigate whether there is a relationship between your chosen explanatory variable and your chosen response variable.
4. State clearly what your chosen explanatory variable (x-axis) is, and what your chosen response variable is (y-axis). Give the units.
5. For merit or excellence, state why you have chosen your explanatory variable and response variable, and how you think your explanatory variable will affect your response variable.
6. For merit or excellence state whether you think there is causation involved (i.e an increase in the explanatory variable, among other things, tends to causes the response variable to increase, e.g. smoking increases the risk of lung cancer) or whether there is merely a statistical relationship (i.e. both of your variables are mutually affected by some other factor e.g. smoking does not cause alcoholism but both are caused by a problem with addiction and may increase together).
7. Show your graph without any trend line. Give it a title, label it and show the units.
8. Does it look like an increase in the explanatory variable coincides with an increase/decrease in the response variable? i.e. Does it look like a positive or negative relationship? Does it look like a linear relationship where the dots tend to form a straight line more or less (or for merit or excellence does it look like something else e.g. quadratic, logarithmic?)
9. Are there any clusters of data between certain areas across the explanatory variable and over a range of the response variable? (For merit and excellence be specific and try to find supporting reason from research).
10. How scattered is the data? Is it more scattered for lower or higher values of the explanatory variable? (Say why for merit or excellence).
7. Show your graph without any trend line. Give it a title, label it and show the units.
8. Does it look like an increase in the explanatory variable coincides with an increase/decrease in the response variable? i.e. Does it look like a positive or negative relationship? Does it look like a linear relationship where the dots tend to form a straight line more or less (or for merit or excellence does it look like something else e.g. quadratic, logarithmic?)
9. Are there any clusters of data between certain areas across the explanatory variable and over a range of the response variable? (For merit and excellence be specific and try to find supporting reason from research).
10. How scattered is the data? Is it more scattered for lower or higher values of the explanatory variable? (Say why for merit or excellence).
11. Mention any outliers on your graph. State what they are e.g. a certain model of car. (For merit or excellence try to give reasons.)
12. For merit or excellence state if there is a stronger relationship between certain ranges of data on your explanatory variable and response variable, and try to give reasons from research.
13. Show your second graph with the linear trend line.
14. State whether you think the linear trend line is a good model for your data, over the whole range, most of the range or part of the range.
15. State whether the data is evenly spaced above and below the trend line for certain ranges or the whole graph, and how scattered or clustered they are in certain areas about the trend line.
16. Write down the equation for the trend line, the correlation coefficient and the sample size.
17. Talk about the y-intercept on the response variable (Get this from the final number on your equation). What does this mean? Is it practical, and does it limit the extent of the model?
12. For merit or excellence state if there is a stronger relationship between certain ranges of data on your explanatory variable and response variable, and try to give reasons from research.
13. Show your second graph with the linear trend line.
14. State whether you think the linear trend line is a good model for your data, over the whole range, most of the range or part of the range.
15. State whether the data is evenly spaced above and below the trend line for certain ranges or the whole graph, and how scattered or clustered they are in certain areas about the trend line.
16. Write down the equation for the trend line, the correlation coefficient and the sample size.
17. Talk about the y-intercept on the response variable (Get this from the final number on your equation). What does this mean? Is it practical, and does it limit the extent of the model?
18. By how much does an increase of 1 in your explanatory variable tend to show an increase/decrease in your response variable? (Eg. For every 1L increase of engine size there tends to be a corresponding increase of 36.2 HP - This is the gradient number on your equation.)
19. Is the strength of the relationship between your explanatory variable and response variable weak, moderate, relatively strong or very strong, and is it positive or negative? Mention that this is supported by your correlation (r) value.
20. For merit and excellence discuss causation again (see step 6 above), and also whether other factors are involved in affecting the response variable from research.
21. For merit and excellence, either split your data into groups/ranges and/or show the graph again with a new trend line (e.g. a quadratic trend line) in order to try to get better r-values and repeat steps 14 to 17 above on each new set of data. Mention what you are doing, why you are doing it, and whether it gives an improvement, i.e. a better fit to the data.
22. Using your equation(s) make predictions (with sensible rounding) for certain values on your explanatory variable for all your models, giving corresponding predictions of where the response values should be, and discussing which model line/curve gives the best estimate/prediction. For merit and excellence link this with reasons and/or research.
19. Is the strength of the relationship between your explanatory variable and response variable weak, moderate, relatively strong or very strong, and is it positive or negative? Mention that this is supported by your correlation (r) value.
20. For merit and excellence discuss causation again (see step 6 above), and also whether other factors are involved in affecting the response variable from research.
21. For merit and excellence, either split your data into groups/ranges and/or show the graph again with a new trend line (e.g. a quadratic trend line) in order to try to get better r-values and repeat steps 14 to 17 above on each new set of data. Mention what you are doing, why you are doing it, and whether it gives an improvement, i.e. a better fit to the data.
22. Using your equation(s) make predictions (with sensible rounding) for certain values on your explanatory variable for all your models, giving corresponding predictions of where the response values should be, and discussing which model line/curve gives the best estimate/prediction. For merit and excellence link this with reasons and/or research.
23. Mention whether your predictions are accurate or not i.e. whether you have confidence in them or not, with reference to how close the existing data (dots) are above or below your prediction, and your correlation value(s). Have at least one reasonably confident prediction if possible and another not so confident.
24. Under the title “Conclusion”, answer your original question, and as to whether there is a positive/negative linear or other relationship between your variables (name them clearly again) and for merit and excellence give reasons and a summary of your findings, and clearly mention what is the extent and limits of your model e.g. due to specific outliers or scatter in various places.
25. For merit and excellence, what could you conclude about the wider population, and why?
26. For merit or excellence mention how you could have improved your model, e.g. by looking into other variables (name them) or by further splitting, gaining more data, using a new model (curve etc), as appropriate.
24. Under the title “Conclusion”, answer your original question, and as to whether there is a positive/negative linear or other relationship between your variables (name them clearly again) and for merit and excellence give reasons and a summary of your findings, and clearly mention what is the extent and limits of your model e.g. due to specific outliers or scatter in various places.
25. For merit and excellence, what could you conclude about the wider population, and why?
26. For merit or excellence mention how you could have improved your model, e.g. by looking into other variables (name them) or by further splitting, gaining more data, using a new model (curve etc), as appropriate.