Presentation is loading. Please wait.

Presentation is loading. Please wait.

4.3.2: Warm-up, P.107 A new social networking company launched a TV commercial. The company tracked the number of users in thousands who joined the network.

Published byMildred Hutchinson Modified over 8 years ago

Similar presentations

Presentation on theme: "4.3.2: Warm-up, P.107 A new social networking company launched a TV commercial. The company tracked the number of users in thousands who joined the network."— Presentation transcript:

1 4.3.2: Warm-up, P.107 A new social networking company launched a TV commercial. The company tracked the number of users in thousands who joined the network after each week the commercial aired. Use the table of data on the next slide to answer the questions that follow. 1 4.3.2: Calculating and Interpreting the Correlation Coefficient

2 2 Number of weeksNew users in thousands 16 29 315 419 5 622 732 831 937 1045 1144

3 1.Create a scatter plot of the data. 3 4.3.2: Calculating and Interpreting the Correlation Coefficient New users in thousandsNumber of weeks

4 2.Does the data appear to have a linear or exponential relationship? Explain. The data appears to have a linear relationship. The shape of the data in the graph is linear because a line could be drawn on the graph with an approximately equal number of points above and below the graph. 4 4.3.2: Calculating and Interpreting the Correlation Coefficient

5 4.3.2: Introduction In previous lessons, we have plotted and analyzed data that appears to have a linear relationship. The data points in some data sets were very close to a linear model, while other data sets had points that were farther from the linear model. The strength of the relationship between data that has a linear trend can be analyzed using the correlation coefficient. 5 4.3.2: Calculating and Interpreting the Correlation Coefficient

6 4.3.2: Key Concepts Correlation: a relationship between two events where a change in one event implies a change in another event. Correlation doesn’t mean that a change in the first event caused a change in the other event. The strength of a linear correlation can be measured using a correlation coefficient. 6 4.3.2: Calculating and Interpreting the Correlation Coefficient

7 Key Concepts, continued Correlation coefficient of –1: indicates a perfect negative correlation. Correlation coefficient of 1: indicates a perfect positive correlation. Correlation coefficient of 0: indicates no linear correlation. The correlation coefficient only assesses the strength of a linear relationship between two variables. The correlation coefficient does not assess causation—that one event causes the other. Example: coefficients -.87 &.87 have equal strength!! 7 4.3.2: Calculating and Interpreting the Correlation Coefficient

8 Correlation Coefficient chart: copy!!! 8 4.3.2: Calculating and Interpreting the Correlation Coefficient -.5 0 +.5 +1.00 Perfect Negative Correlation Strong Neg. Corr. Moderate Neg. Corr. Weak Neg. Corr. NO Correlation Weak Pos. Corr. Moderate Pos. Corr. Strong Pos. Corr. Perfect Positive Correlation negative correlation positive correlation -.75 -.25 +.25 +.75

9 No relation: 9 4.3.2: Calculating and Interpreting the Correlation Coefficient Annual income # of children Weak, Negative Corr. Strong, Positive Corr. High School GPA College GPA Price ($) Quantity Sold Some form of technology is needed to calculate the Correlation Coefficient. Wolfram web site: “Pearson’s Correlation Coefficient Calculator” www.easycalculation.com/statistics/correlation.php Or www.desmos.comwww.desmos.com Or www.socscistatistics.com/tests/pearson/default2.aspx www.socscistatistics.com/tests/pearson/default2.aspx

10 Common Errors/Misconceptions using the correlation coefficient to analyze data that is not linear incorrectly using the correlation coefficient to assess the strength of a relationship 10 4.3.2: Calculating and Interpreting the Correlation Coefficient

11 Guided Practice Example #1: An education research team is interested in determining if there is a relationship between a student’s vocabulary and how frequently the student reads books. The team gives 20 students a 100-question vocabulary test, and asks students to record how many books they read in the past year. The results are in the table on the next slide. Is there a linear relationship between the number of books read and test scores? Use the correlation coefficient, r, to explain your answer. 11 4.3.2: Calculating and Interpreting the Correlation Coefficient

12 Guided Practice: Example #1, continued 12 4.3.2: Calculating and Interpreting the Correlation Coefficient Books readTest scoreBooks readTest score 1223512 831530 1914836 98519 145610 19 1363 152549 6301678 2616 144279

13 Guided Practice: Example #1, continued 1.Create a scatter plot of the data. Let the x-axis represent books read and the y-axis represent test score. 13 4.3.2: Calculating and Interpreting the Correlation Coefficient

14 Guided Practice: Example #1, continued 14 4.3.2: Calculating and Interpreting the Correlation Coefficient Test score Books read

15 Guided Practice: Example #1, continued 2.Describe the relationship between the data using the graphical representation. It appears that the higher scores were from students who read more books, but the data does not appear to lie on a line. There is not a strong linear relationship between the two events. 15 4.3.2: Calculating and Interpreting the Correlation Coefficient

16 Guided Practice: Example #1, continued 3.Calculate the correlation coefficient on your graphing calculator. Refer to the website in the Key Concepts section. The correlation coefficient, r, is approximately 0.48. 16 4.3.2: Calculating and Interpreting the Correlation Coefficient

17 Guided Practice: Example #1, continued 4.Use the correlation coefficient to describe the strength of the relationship between the data. A correlation coefficient of 1 indicates a strong positive correlation, and a correlation of 0 indicates no correlation. A correlation coefficient of 0.48 is about halfway between 0 and 1, and indicates that there is a moderate positive linear relationship between the number of books a student read in the past year and his or her score on the vocabulary test. 17 4.3.2: Calculating and Interpreting the Correlation Coefficient ✔

18 Guided Practice Example #3: Caitlyn thinks that there may be a relationship between class size and student performance on standardized tests. She tracks the average test performance of students from 20 different classes, and notes the number of students in each class in the table on the next slide. Is there a linear relationship between class size and average test score? Use the correlation coefficient, r, to explain your answer. 18 4.3.2: Calculating and Interpreting the Correlation Coefficient

19 Guided Practice: Example #3, continued 19 4.3.2: Calculating and Interpreting the Correlation Coefficient Class sizeAvg. test scoreClass sizeAvg. test score 26283233 36252730 29272133 26322827 19382341 34322928 17433723 14421439 23372531 17413330

20 Guided Practice: Example #3, continued 1.Create a scatter plot of the data. Let the x-axis represent the number of students in each class and the y-axis represent the average test score. 20 4.3.2: Calculating and Interpreting the Correlation Coefficient

21 Guided Practice: Example #3, continued 21 4.3.2: Calculating and Interpreting the Correlation Coefficient Average test score Number of students

22 Guided Practice: Example #3, continued 2.Describe the relationship between the data using the graphical representation. As the class size increases, the average test score decreases. It appears that there is a linear relationship with a negative slope between the two variables. 22 4.3.2: Calculating and Interpreting the Correlation Coefficient

23 Guided Practice: Example #3, continued 3.Calculate the correlation coefficient on your graphing calculator. Refer to the website in the Key Concepts section. The correlation coefficient, r, is approximately –0.84. 23 4.3.2: Calculating and Interpreting the Correlation Coefficient

24 Guided Practice: Example #3, continued 4.Use the correlation coefficient to describe the strength of the relationship between the data. A correlation coefficient of –1 indicates a strong negative correlation, and a correlation of 0 indicates no correlation. A correlation coefficient of –0.84 is close to –1, and indicates that there is a strong negative linear relationship between class size and average test score. 24 4.3.2: Calculating and Interpreting the Correlation Coefficient ✔

25 Homework Workbook(4.3.2):, P.115 # 1-10 25

Download ppt "4.3.2: Warm-up, P.107 A new social networking company launched a TV commercial. The company tracked the number of users in thousands who joined the network."

Similar presentations

Introduction When linear functions are used to model real-world relationships, the slope and y-intercept of the linear function can be interpreted in context.

Introduction When linear functions are used to model real-world relationships, the slope and y-intercept of the linear function can be interpreted in context.
Describing the Relation Between Two Variables

Describing the Relation Between Two Variables
Calculating and Interpreting the Correlation Coefficient ~adapted from walch education.

Calculating and Interpreting the Correlation Coefficient ~adapted from walch education.
Ms. Albarico Often, when real-world data is plotted, the result is a linear pattern. The general direction of the data can be seen, but the data points.

Ms. Albarico Often, when real-world data is plotted, the result is a linear pattern. The general direction of the data can be seen, but the data points.
Introduction Tables and graphs can be represented by equations. Data represented in a table can either be analyzed as a pattern, like the data presented.

Introduction Tables and graphs can be represented by equations. Data represented in a table can either be analyzed as a pattern, like the data presented.
Chapter 13 Statistics © 2008 Pearson Addison-Wesley. All rights reserved.

Chapter 13 Statistics © 2008 Pearson Addison-Wesley. All rights reserved.
Introduction A correlation between two events simply means that there is a consistent relationship between two events, and that a change in one event implies.

Introduction A correlation between two events simply means that there is a consistent relationship between two events, and that a change in one event implies.
© 2008 Pearson Addison-Wesley. All rights reserved 13-6-1 Chapter 1 Section 13-6 Regression and Correlation.

© 2008 Pearson Addison-Wesley. All rights reserved Chapter 1 Section 13-6 Regression and Correlation.
Introduction When linear functions are used to model real-world relationships, the slope and y-intercept of the linear function can be interpreted in context.

Introduction When linear functions are used to model real-world relationships, the slope and y-intercept of the linear function can be interpreted in context.
Correlation Analysis. A measure of association between two or more numerical variables. For examples height & weight relationship price and demand relationship.

Correlation Analysis. A measure of association between two or more numerical variables. For examples height & weight relationship price and demand relationship.
Chapter 10 10-1. Bivariate Data (x,y) data pairs Plotted with Scatter plots x = explanatory variable; y = response Bivariate Normal Distribution – for.

Chapter Bivariate Data (x,y) data pairs Plotted with Scatter plots x = explanatory variable; y = response Bivariate Normal Distribution – for.
Creating a Residual Plot and Investigating the Correlation Coefficient.

Creating a Residual Plot and Investigating the Correlation Coefficient.
Section 5.1: Correlation. Correlation Coefficient A quantitative assessment of the strength of a relationship between the x and y values in a set of (x,y)

Section 5.1: Correlation. Correlation Coefficient A quantitative assessment of the strength of a relationship between the x and y values in a set of (x,y)
Correlation The apparent relation between two variables.

Correlation The apparent relation between two variables.
Solving Problems Given Functions Fitted to Data/Interpreting Slope and y-intercept Key Terms: Linear Fit Slope Scatter Plot 1 4.6: Solving Problems Given.

Solving Problems Given Functions Fitted to Data/Interpreting Slope and y-intercept Key Terms: Linear Fit Slope Scatter Plot 1 4.6: Solving Problems Given.
We would expect the ENTER score to depend on the average number of hours of study per week. So we take the average hours of study as the independent.

We would expect the ENTER score to depend on the average number of hours of study per week. So we take the average hours of study as the independent.
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 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.
Correlations AP Psychology. Correlations  Co-relation  It describes the relationship b/w two variables.  Example #1  How is studying related to grades?

Correlations AP Psychology. Correlations  Co-relation  It describes the relationship b/w two variables.  Example #1  How is studying related to grades?
Lesson 4.7 – Interpreting the Correlation Coefficient and Distinguishing between Correlation & Causation EQs: How do you calculate the correlation coefficient?

Lesson 4.7 – Interpreting the Correlation Coefficient and Distinguishing between Correlation & Causation EQs: How do you calculate the correlation coefficient?
.  Relationship between two sets of data  The word Correlation is made of Co- (meaning together), and Relation  Correlation is Positive when the.

.  Relationship between two sets of data  The word Correlation is made of Co- (meaning "together"), and Relation  Correlation is Positive when the.

Similar presentations

Ads by Google