Correlation S1 Maths with Liz.

Slides:

Advertisements

Similar presentations

Section 10-3 Regression.

Advertisements

Scatterplots and Correlation

3.1b Correlation Target Goal: I can determine the strength of a distribution using the correlation. D2 h.w: p 160 – 14 – 18, 21, 26.

Linear regression and correlation

2-7 Curve Fitting with Linear Models Warm Up Lesson Presentation

Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and.

Bivariate Data – Scatter Plots and Correlation Coefficient…… Section 3.1 and 3.2.

Section 7.1 ~ Seeking Correlation

Correlation Scatter Plots Correlation Coefficients Significance Test.

Is there a relationship between the lengths of body parts ?

Measure your handspan and foot length in cm to nearest mm We will record them as Bivariate data below: Now we need to plot them in what kind of graph?

Correlation and regression lesson 1 Introduction.

Warm-up with 3.3 Notes on Correlation

Researchers, such as anthropologists, are often interested in how two measurements are related. The statistical study of the relationship between variables.

Warm-up with 3.3 Notes on Correlation Universities use SAT scores in the admissions process because they believe these scores provide some insight into.

Correlation 1 Scatter diagrams Measurement of correlation Using a calculator Using the formula Practice qs.

Warm Up Write the equation of the line passing through each pair of passing points in slope-intercept form. 1. (5, –1), (0, –3) 2. (8, 5), (–8, 7) Use.

Section 4.1 Scatter Diagrams and Correlation. Definitions The Response Variable is the variable whose value can be explained by the value of the explanatory.

Scatterplots are used to investigate and describe the relationship between two numerical variables When constructing a scatterplot it is conventional to.

Relationships If we are doing a study which involves more than one variable, how can we tell if there is a relationship between two (or more) of the.

Chapter Bivariate Data (x,y) data pairs Plotted with Scatter plots x = explanatory variable; y = response Bivariate Normal Distribution – for.

2-7 Curve Fitting with Linear Models Warm Up Lesson Presentation

Correlation The apparent relation between two variables.

Scatter Diagram of Bivariate Measurement Data. Bivariate Measurement Data Example of Bivariate Measurement:

2.5 Using Linear Models A scatter plot is a graph that relates two sets of data by plotting the data as ordered pairs. You can use a scatter plot to determine.

2.5 Using Linear Models P Scatter Plot: graph that relates 2 sets of data by plotting the ordered pairs. Correlation: strength of the relationship.

AP Statistics HW: p. 165 #42, 44, 45 Obj: to understand the meaning of r 2 and to use residual plots Do Now: On your calculator select: 2 ND ; 0; DIAGNOSTIC.

Section Copyright © 2014, 2012, 2010 Pearson Education, Inc. Chapter 10 Correlation and Regression 10-2 Correlation 10-3 Regression.

Mathematical Studies for the IB Diploma © Hodder Education Pearson’s product–moment correlation coefficient.

Graph of Function EquationGradientY-intercept A B C D E F G H I J.

CORRELATION ANALYSIS.

ContentDetail  Two variable statistics involves discovering if two variables are related or linked to each other in some way. e.g. - Does IQ determine.

Correlation Assumptions: You can plot a scatter graph You know what positive, negative and no correlation look like on a scatter graph.

Chapter 9 Scatter Plots and Data Analysis LESSON 1 SCATTER PLOTS AND ASSOCIATION.

Correlation Lesson 2 Aims: To be able to calculate the PMCC, r, given summarised data. To know that the value of the PMCC is unchanged by linear coding.

GOAL: I CAN USE TECHNOLOGY TO COMPUTE AND INTERPRET THE CORRELATION COEFFICIENT OF A LINEAR FIT. (S-ID.8) Data Analysis Correlation Coefficient.

REGRESSION Stats 1 with Liz. AIMS By the end of the lesson, you should be able to… o Understand the method of least squares to find a regression line.

Correlation & Linear Regression Using a TI-Nspire.

Chapter 2 Bivariate Data Scatterplots.   A scatterplot, which gives a visual display of the relationship between two variables.   In analysing the.

Review and Preview and Correlation

Warm Up Scatter Plot Activity.

Is there a relationship between the lengths of body parts?

MATH 2311 Section 5.1 & 5.2.

Objectives Fit scatter plot data using linear models with and without technology. Use linear models to make predictions.

Chapter 4 Correlation.

Scatterplots A way of displaying numeric data

Correlation At a tournament, athletes throw a discus. The age and distance thrown are recorded for each athlete: Do you think the distance an athlete.

Statistics for the Social Sciences

Exercise 4 Find the value of k such that the line passing through the points (−4, 2k) and (k, −5) has slope −1.

Describing Bivariate Relationships

2. Find the equation of line of regression

2.6 Draw Scatter Plots and Best-Fitting Lines

A correlation is a relationship between two variables. 

Lecture Notes The Relation between Two Variables Q Q

CORRELATION ANALYSIS.

Introduction to Probability and Statistics Thirteenth Edition

Section 1.4 Curve Fitting with Linear Models

Chapter 4 - Scatterplots and Correlation

11A Correlation, 11B Measuring Correlation

11C Line of Best Fit By Eye, 11D Linear Regression

September 25, 2013 Chapter 3: Describing Relationships Section 3.1

Objectives Vocabulary

Homework: pg. 180 #6, 7 6.) A. B. The scatterplot shows a negative, linear, fairly weak relationship. C. long-lived territorial species.

Describing Bivariate Relationships

Processing and Representing Data

7.1 Draw Scatter Plots and Best Fitting Lines

Correlation & Trend Lines

Section 11.1 Correlation.

Presentation transcript:

Correlation S1 Maths with Liz

AIMS By the end of the lesson, you should be able to… Draw scatter graphs & understand correlation Understand causality Calculate & use the PMCC Understand the limitations of using the PMCC

Correlation Bivariate data is data that has two variables. Scatter graphs are often used to show a relationship or correlation between two random variables. The stronger the correlation, the more closely related the two variables are likely to be.

Key terms

Product Moment Correlation Coefficient (PMCC) The product–moment correlation coefficient gives a numerical measure of the strength of the linear association between two variables. The PMCC is represented by the letter r and must lie between -1 and 1. r = 1 indicates perfect linear positive correlation; r = 0 indicates that there is absolutely no linear correlation between the variables. r = -1 indicates perfect linear negative correlation;

How to describe your value for r… Some suggested descriptions of correlation are: When r is between -0.2 and 0.2, the correlation is very weak. When r is between 0.2 and 0.7, or between -0.2 and -0.7, the correlation is moderate. When r is between 0.7 and 0.9, or between -0.7 and -0.9, the correlation is strong. When r is between 0.9 or below -0.9, the correlation is very strong.

How to calculate the PMCC. The product–moment correlation coefficient for n pairs of observations is obtained using the formula: ALL of these formulae are given on pg. 13! where: Usually, the second version of each formula is used because we can find these values using our calculators!

Example 1 A teacher measures & records the heights (in cm) and hand spans (in inches) of 10 boys in year 8. (a) Plot the data on a scatter diagram. (b) Calculate the product moment correlation coefficient. (c) Describe the relationship that exists between the two variables.

Example 1 (a) Plot the data on a scatter diagram. A teacher measures & records the heights (in cm) and hand spans (in inches) of 10 boys in year 8.

Let’s start by finding each piece separately with the use of our GDC. Example 1 (b) Calculate the product moment correlation coefficient. A teacher measures & records the heights (in cm) and hand spans (in inches) of 10 boys in year 8. Open your AQA formulae booklets to pg. 13. Let’s start by finding each piece separately with the use of our GDC. In your GDC, press MENU STAT enter data in lists 1 and 2 CALC (F2) check settings to make sure your 2VAR Freq: 1, then EXE 2 VAR (F2)

Let’s start by finding each piece separately with the use of our GDC. Example 1 (b) Calculate the product moment correlation coefficient. A teacher measures & records the heights (in cm) and hand spans (in inches) of 10 boys in year 8. Open your AQA formulae booklets to pg. 13. Let’s start by finding each piece separately with the use of our GDC.

Let’s start by finding each piece separately with the use of our GDC. Example 1 (b) Calculate the product moment correlation coefficient. A teacher measures & records the heights (in cm) and hand spans (in inches) of 10 boys in year 8. Open your AQA formulae booklets to pg. 13. Let’s start by finding each piece separately with the use of our GDC.

Now, bring it all back together using the formula for r. Example 1 (b) Calculate the product moment correlation coefficient. A teacher measures & records the heights (in cm) and hand spans (in inches) of 10 boys in year 8. Now, bring it all back together using the formula for r.

Example 1 (c) Describe the relationship that exists between the two variables. A teacher measures & records the heights (in cm) and hand spans (in inches) of 10 boys in year 8. There is a strong positive correlation between hand length and height, meaning that the height increases as the hand length increases.

Finding r directly in the GDC… You can calculate r directly in your calculator. HOWEVER, sometimes the exam will give you summarised data where you must use the formulae to work out the answers. In your GDC, press MENU STAT enter data in lists 1 and 2 CALC (F2) REG (F3) X (F1) a + bx (F2) look for the r value

Plotting Scatter Graphs in your GDC… You can plot your scatter graphs in your graphing calculator also! In your GDC, press MENU STAT enter data in lists 1 and 2 GRPH (F1) Check the settings to make sure Graph Type: Scatter, then EXE GPH1 (F1)

Limitations of the PMCC The product–moment correlation coefficient (PMCC) measures the strength of a linear relationship. However: Outliers can greatly distort the PMCC; The PMCC is not a suitable measure of correlation if the relationship is non-linear. This graph would give a PMCC of around 0, meaning no correlation. BUT there is clearly a pattern (quadratic). It is always best to make a sketch of the data to check if there is another sort of pattern.

Linear Scaling – does this affect the pmcc? Let’s go back to EXAMPLE 1. A teacher measures & records the heights (in cm) and hand spans (in inches) of 10 boys in year 8. (a) Calculate the product moment correlation coefficient of the new data.

Linear Scaling – does this affect the pmcc? (b) How did converting the hand length from in. to cm. affect the scatter plot and product moment correlation coefficient of the new data? The PMCC is still 0.9432.

Example 2 – Summarised data January 2013, q.4 Possible responses could include: identify any outliers identify any linear or non-linear relationships or patterns use the scatter plot to estimate the value & sign of r

Example 2 – Summarised data January 2013, q.4

Example 2 – Summarised data January 2013, q.4 There is a moderate positive correlation between the two statistics exam marks.

Example 2 – Summarised data January 2013, q.4 ruv should be equal to rxy because linear scaling has no affect on the value of r (the PMCC).

Independent Study REVISE REVISE REVISE!!!!!!! Go through all questions related to correlation in your stats 1 past paper booklet. HEAVILY RECOMMENDED: mymaths – scatter graphs mymaths – product moment correlation coefficient (just do the PMCC questions. Don’t worry about filling in the tables…they are there for folks who don’t have a graphing calculator). Stats Textbook: Pg. 149, Ex. 6A Stats Textbook: Pg. 155, Ex. 6B MEI WS – “AQA Stats 1 Correlation and regression, Section 1: Correlation”