IB Math Studies Yr 1

Name_________________________________ Date: ____________

Lesson 3-2: Correlation Coefficient Learning Goals:

#1: What is the correlation coefficient and how do I interpret a correlation coefficient? #2: How do I calculate the correlation coefficient given a list of data?

Warm-Up: 1. Below is a scatterplot that displays the association between the size of a diamond (in carats) and its retail

price.

Describe in your own words the relationship that you see between to the two variables using words from the

word bank on the right of the scatterplot.

When looking at a scatterplot there are THREE concepts you must discuss Direction Strength

Word Bank:

Positive Negative Increase

Decrease Strong Weak

Linear Non Linear

IB Math Studies Yr 1

Linearity

Matching Activity: With a partner, match each of the given scatterplots with their corresponding description

of the correlation. Be ready to justify your pairs!

Word Bank

a. Positive, strong, , linear

b. Negative, strong, linear

c. No correlation

d. Positive, moderate, linear

e. Negative, moderate, linear

f. Positive, weak, linear

g. Negative, weak, linear

h. Positive, strong, non-linear

i. Negative, strong, non-linear

IB Math Studies Yr 1

How does IB ask this question? 1) Describe the relationship between the two variables shown in each of the scatter diagrams below.

Working:

Answers:

(a) ………………………………………………………………..

(b) ………………………………………………………………..

(c) ………………………………………………………………..

(d)………………………………………………………………...

(Total 4 marks)

10

8

6

4

2

10

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6

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2

10

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4

2

10

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6

4

2

0

0

0

0

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2

2

2

4

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4

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10

10

10

10

x

x

x

x

y

y

y

y

(a)

(c)

(b)

(d)

IB Math Studies Yr 1

Determining/Interpreting the Correlation Coefficient.

Steps:

1. Type your data intoL1 and L2

2. Stat -> Calc

3. Option 4: LinReg(ax + b)

Class Example Use your calculator to determine the correlation Coefficient for the data below.

Interpreting the Correlation Coefficient

Correlation Coefficient

A numerical measurement used to determine the ____________________ and ___________________ of a ______________ relationship (Strong/Weak) (positive/negative) (*Note* Shape will always be linear because you used a linear regression) Facts about r: Now interpret the correlation coefficient that you calculated in the class example above:

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=0CAcQjRw&url=http://www.mathcaptain.com/statistics/pearson-correlation-coefficient.html&ei=kZJWVI2CPdT9oQTl-YHQBw&bvm=bv.78677474,d.aWw&psig=AFQjCNHfJ9IR7NplyRlIhvQ4rXpGOJ3gAw&ust=1415046150424815

IB Math Studies Yr 1

More Examples of IB Questions with Correlation Coefficients: 1. The table below shows the minimum hourly wage, in U.S. dollars, for selected years since 1955.

a. Calculate the correlation coefficient.

b. Based on your answer to part a, describe the relationship between years since 1955 and minimum

wage.

Putting it all Together:

2. Erica, the manager at Stellarbeans, collected data on the daily high temperature and revenue from coffee sales. Data from nine days this past fall are shown in the table below.

a. What was the mean of the daily high temperature over the past 9 days?

b. What was the standard deviation of coffee sales over the past 9 days?

c. Calculate the correlation coefficient, and describe what this means in terms of the daily high temperature and coffee sales?

IB Math Studies Yr 1

Name_________________________________ Date: ____________

Lesson 3-2 Homework

1. The table below shows the attendance at a museum in select years from 2007 and 2013.

a. State the Pearson’s Correlation Coefficient.

b. What does this value suggest about the relationship between the two variables?

2. The percentage of students scoring 85 or better on a mathematics final exam and an English exam

during a recent school year for seven schools is shown in the table below.

a. State and clearly label the mean Mathematics and English scores.

b. State and clearly label the standard deviation of Mathematics and English scores.

c. Calculate the correlation coefficient, and interpret this statistic.

IB Math Studies Yr 1 3. The mean of the eleven numbers listed below is 9. The mode is 7.

5, 6, 6, 7, 7, 𝑎, 9, 11, 11, 14, 𝑏

a. Find the value of a.

b. Find the value of b.

c. Calculate the median of the list of numbers.

4. Statements I, II, III, IV and V represent descriptions of the correlation between two variables. I High positive linear correlation II Low positive linear correlation III No correlation IV Low negative linear correlation V High negative linear correlation Which statement best represents the relationship between the two variables shown in each of the scatter diagrams below?

Answers:

(1) ______________

(2) ______________

(3) ______________

(4) ______________