Bivariate+Data


 * Bivariate Data 13MF **

I have put various data sets in the Shared Documents 13MF folder. Generally you need to get students used to Note: you can also mention the r value here (also know as the correlation coefficient) The work in the booklet supports this but does not go through these points step by step.
 * **writing a Purpose Statement,**
 * Eg:To investigate the relationship between the response variable (y axis) NAME and the explanatory variable (x axis) NAME then put in context.
 * **plotting a scatter graph,**
 * **visually describing the scatterplot**, and justify everything, ie. why it's positive/negative (eg:because as the length increases the weight also tends to increase), strength & linear shape (eg: because the scatter plots are very close toghether and are increasing in a positive direction and are close to an imaginary linear trend line)
 * 1) Weak to moderate negative linear relationship between... (r =-0.5)
 * 2) Strong negative linear relationship between... (r = -.09)
 * 3) Moderate positive linear... (r =0.7)
 * 4) Very strong positive linear... (r =0.95)
 * **fitting a regression line (trendline)**
 * **Giving a full quantitative description, in context, of what the regression model is telling us about the variables**
 * **Must have a conclusion!**

Here is an outline of what is expected

=**Lessons for 2013:**=


 * 2nd to 4th July:**
 * **Read through the 'Exemplar of Student work' above (carefully!)**
 * **Use your orange Bivariate booklet to help you (pgs 7-9)**
 * **Try these practice examples. Write a purpose statement, graph it, find the trendline and R squared value, then describe the data. (see the 'Alligator data answers for an example).**
 * **Try and finish the other data sets :)**

= = = = =  = == =5 & 8 July= (I will show you two graphs from yesterday on the board today during the lesson) One is here:
 * Making Predictions**

To make a prediction you use an 'x' value ONLY; so we will predict what the y value is. Interpolation means it can be seen on your graph; extrapolation means it can not be seen off your graph.

Simply use your equation to make any predictions and replace the x value (don't forget to multiply it by the number in front!). You can use 'equation solver' in your calculator to solve y.

You can discuss how 'reliable' your predictions are because of how 'strong' the relationship is between the variables (including the r value).

R is the measure of how closely the data points fit the regression line (or, trendline).
 * PLEASE NOTE THAT TO FIND THE CORRELATION CO-EFFIENT OR R VALUE, SQUARE ROOT THE R² VALUE FROM THE EQUATION. **


 * 10th July**

You were given an example of a conclusion to stick in your Orange booklet (from p53 of your HW book). Read it carefully (we will go over this in class) then finish off the written work for 'Alcohol and Tobacco Spending' that we started yesterday (including writing a conclusion).


 * We have covered everything you need to complete this Internal to achieve level.**

HOMEWORK: Email me (nathans@freyberg.ac.nz) OR print your graph and written work for Alcohol and Tobacco spending!

When you have completed 'Alcohol and Tobacco' Work on the next lot of Data - 'Identical Twins'

**11 and 12 July**
You will be handed information on what it is you are investigating. The data you are using is here:
 * Finish this Practice Assessment.**

Your response variable must be 'Ice cream'; you only select an appropriate explanatory variable from the other 4 variables available. If you find that there is no relationship when you create your graph; choose another variable. Use you orange booklets to help you. Good luck.


 * 28 July to 1 August - Finish the Bamboo task today (1 August) and send it to me or print it so I can give you feedback.**
 * We are going to work on going through each step you need to complete your assessment (next week!).
 * You will be handed out exemplars to keep somewhere safe (remember this assessment is also 'open book' and you will be required to do some research (like for time-series).
 * If you did not finish the 'ice-cream' task above this needs to be done (get info sheet from me).
 * If you are finished you can work on this practise assessment (PS: this will be need to be handed in by the end of the week, it's down as your HW).[[file:Bivariate Prac Assessment 08.doc]][[file:Copy of bamboo data for Bivariate Prac Ass..xlsx]]
 * When completed you can work on pracitising on this McDonalds data: [[file:McDonaldsTM Nutrition Information.xls]]
 * **If you are finished you can choose to practice on some more data (use the Identical twins or mammal gestation period) above, under 10 July.**


 * 2 August**
 * You should have completed the bamboo prac. assessment and given me a copy of it/or sent it to me.
 * Today you can continue to practice your written pieces for the McDonald's data above. Go through each of the steps: Purpose Statement, Description, Predictions, Conclusion and remember to justify everything!
 * If you manage to finish that you can practise on the Identical twins or mammal gestation data above (beneath 10 July work)


 * 5 to 7 August (Mon - Wed). Those who owe $2 need to get that in ASAP.**
 * Final Prac Assessment before the real thing. Here is the question/info sheet followed by the data. [[file:Crime Pays Activity 90645 .doc]][[file:Crime Pays  Data.xls]]

See me if you are unsure about any of the steps you need to work through.
 * You should all have the topic for our assessment for this week. Libby-Anne & Kieran need to get the research sheet from me today.

=**Library Lessons:**= Eg: A strong, positive, linear trend.
 * Here are some model answers for you to check:**
 * 27 Aug**
 * Read through first 4 pages of booklet and make sure you have a good understanding about how to 'describe' scatter plots.
 * Describe the Scatter Plots on P5, then rank the scatter plots on P6.
 * Complete P7 (headed Introduction 97) THEN, use excel to create the scatter plot see notes for timeseries to help.


 * 28 Aug**
 * Finish your graph on excel, ensure you have a title, have labelled the axes and have created a trendline and equation.
 * In the equation you will find the gradient (the value in front of the x term) and the Regression value (R²).
 * To find the mean, type in =average( next to the column you want to find the mean for and then highlight the entire column. Then, close bracket and press =. Do the same for both (you may want to copy and paste the first column somewhere).
 * On the next page headed 'Predictor and Response Variable' read the notes and complete the page. You need to understand that the Predictor (x axis) determines the Response Variable (y axis) usually (sometimes there is no predictor or response variable they are just associated Eg: Exam score in Maths and Exam score in English.
 * 29 Aug**
 * We will be going over 'Purpose Statements' creating a template that you can use (you are allowed to take an A4 sheet into your exam). We will continue to go through what is required for Achieve and Merit.Open a word doc. and start making your Bivariate Exam sheet by adding a 'Purpose Statement' that you can refer to. Also add an example of how you might comment on a graph (include Explanatory/Response Variable and how close the points are to the Regression line).
 * Understand the Regression line (R²). The closer R²is to 1 the more reliable estimates will be because of the better fit of the observations to the Regression line and you can make predictions with confidence (See p7 and 8 for info.)
 * Go back to the work/graph from 'Introduction P97' and create a Purpose Statement, Decide if there is a Predictor (Explanatory) and write a summary/conclusion for your results (be aware of what is needed to gain Merit). **See the Exemplar of student work at the top of this page.**


 * 30 Aug**
 * Do page 236 of booklet. ie: guess the R value depending on the scatter plots. Then, write a statement to desribe the relationship of the predictor and explanatory value. Eg: a Strong postive linear relationship between ...... and.......... As ..... increases .......................... increases.
 * Now go into 'Shared docs' and use the data under the heading 'Aligator' and go through these steps (Achieve Steps) OR DOWNLOAD IT HERE: [[file:3Alligator with no graph.xls]]

Now work through these ACHIEVE steps: Here is a model answer for the Aligator data:
 * 1) Write a purpose statement
 * 2) graph displaying the date for the variables chosen
 * 3) Write a regression model for the variables and relate it to your graph
 * 4) Write a full description of the relationship between the variables including an interpretation of what the regression moel tells us about the relationship between the variables.


 * 31 Aug**
 * PLEASE NOTE THAT TO FIND THE R VALUE, SQUARE THE R² VALUE FROM THE EQUATION. R IS THE MEASURE OF HOW CLOSELY THE DATA POINTS FIT THE REGRESSION LINE. EG: IF THE R VALUE IS 0.4733, IT MEANS THAT THE REGRESSION MODEL IS WEAK THEREFORE ANY PREDICTIONS MADE WOULD BE OF LITTLE VALUE. THIS CAN ALSO BE SEEN ON MY GRAPH AS THE PLOTS ARE NOT VERY CLOSE TO THE REGRESSION LINE. THIS MODEL ALSO HAS A 47% (2SF) VARIABILITY ACCOUNTED FOR, HOWEVER, THIS MEANS THAT THE REMAINING 53% IS DUE TO RANDOM FACTORS.**

Make sure you have completed the work above (yesterday's Alligator task)
 * Now, do the same four steps above for this data on Sand Errosion: [[file:5Sand Erosion.xls]]


 * 1) Write a purpose statement
 * 2) graph displaying the date for the variables chosen
 * 3) Write a regression model for the variables and relate it to your graph
 * 4) Write a full description of the relationship between the variables including an interpretation of what the regression moel tells us about the relationship between the variables.

If you were away catch up on our previous lesson (31 Aug) in your own time; this is our last week on the computers.
 * 4 September**
 * We are working on a McDonalds task but this time you must select the two variables. Choose a predictor variable and a response variable (that is determined by the predictor). Eg: Height of a person (generally) determines the weight of a person.


 * Now go through the 4 steps you need for 'Achieve' (see lesson above)

Complete any above work you have not done. Finish your 'cheat sheet' to take in to the exam with you. Once you have completed the above you could start work on this data: And, do what you did on 4th Sep (see lesson above).
 * 5 Sep and 6 Sep**

= You may want to add this to your cheat sheet: = Variables identified Regression line derived and equation given Two or more graphs displaying data (only 1 graph for A) || At least one pair of variables for achieve Regression line and equation for at least one pair of variables for achieve At least one graph for achieve. Allow minor errors in titles and labels || A detailed description in context || Regression model given for achieve Detailed description of relationship between one pair of variables for achieve. ||
 * **Evidence** || **Judgement** ||
 * Purpose statement clearly stated
 * Models for regression and correlation co-efficient given for each of the two variables

I would also copy the table on Interpretation of r And R² on Pg 8 of your booklet as you will need to describe your r value and you can use the predictor comments that are given.
What you need for Merit:
 * 7 Sep**
 * Practcise Assessment:[[file:Bivariate Prac Assessment 08.doc]]**
 * Bamboo Data for Prac. Ass.[[file:Copy of bamboo data for Bivariate Prac Ass..xlsx]]**
 * Make sure you have completed all the lessons above AND that your 'cheat sheet' is good to go. Anyone working towards Merit needs to use their booklets and go through the Merit work (everything but Residule) and also see me.**
 * Here are the answers for the Prac. Assessment above for you to check:[[file:Copy of Bamboo Shoots Data Answers for Prac Ass.xls]]**
 * Discuss the appropriateness of the model Comments
 * Interpreting correlation coefficients, r, and coefficients of determination, R², when appropriate.
 * Discuss the difference between correlation and causality when appropriate (P9 and 10)
 * Making Predictions (and justify their reliability with that model using interpolation and extrapolation (P10)
 * Comparing the relationship between more than one pair of variables (P10).