Lesson on Linear Correlation

Correlation and Correlation Coefficient

​November 30, 2023

Types of Correlation

• Positive

• Negative

• No Correlation

Multiple Choice

What type of correlation does this graph have?

• positive
• negative
• none
• all of the above

Multiple Choice

What type of correlation does this scatter plot show?

• Positive correlation

• Negative correlation

• No correlation

• Constant correlation

Multiple Choice

What type of correlation does this scatter plot show?

• Positive correlation

• Negative correlation

• No correlation

• Constant correlation

• It always has a value between -1 and 1

• Strong positive linear relationships have values of r closer to 1.

• Strong negative linear relationships have values of r closer to -1.

• Weaker relationships have values of r closer to 0.

​What is a correlation coefficient?

The correlation coefficient r measures the direction and strength of a linear relationship. Since, calculation r is difficult we use the calculator.

Multiple Choice

A strong positive correlation has a correlation coefficient of ____. 

• 1
• -1
• 0

Multiple Choice

A strong negative correlation has a correlation coefficient of ____. 

• 1
• -1
• 0

Multiple Choice

Estimate the correlation coefficient for this scatterplot.

• A) r = -0.9

• B) r = 1

• C) r = 0.9

• D) r = -1

Multiple Choice

Estimate the correlation coefficient for this scatterplot.

• r = 1.2
• r = 0.89
• r = 0
• r = -0.89

Multiple Choice

Which graph depicts the strongest positive correlation?

Multiple Choice

r=-0.89

• Strong positive 
• Weak positive 
• Strong negative 
• Weak negative 

Equation- Line of Best Fit

Trend Line

Multiple Choice

Which graph shows a line that best fits the data?

Multiple Choice

Which graph shows a line that best fits the data?

Multiple Choice

Which of the following lines represent the line of best fit for the scatter plot.

• A

• B

• C

• D

Multiple Choice

Which of the following lines represents the line of best fit for the scatter plot?

• A

• B

• C

• D

Correlation Coefficient and Equation of Line

• Turn on Diagnostics

• [2nd], [0], [DiagnosticOn], [Enter] and [Done]

• [STAT]. [Edit], Input table values, [STAT], Calc, [4-LinReg]

• y=ax+b and r=

Let's Practice

[STAT], [Edit], Input table values, [STAT], Calc, [4-LinReg]
y=ax+b, and r=

Let's Practice

[STAT], [Edit], Input table values, [STAT], Calc, [4-LinReg]
y=ax+b, and r=

Multiple Choice

Using your graphing calculator determine the line of best fit and the correlation coefficient of the data in the table.

• y = 4.6x - 347

  r = .942

• y = 4.6x - 347

  r = .888

• y = 4.6x + 347

  r = .942

• y = 4.6x + 347

  r = .888

Multiple Choice

What is the correlation coefficient of the data characteristics shown?

• -.928

• .928

• .861

• -.861

Multiple Choice

As shown in the table, a person's target heart rate during exercise changes as the person gets older. Use the graphing calculator to find the correlation coefficient (r).

• -0.999

• -0.664

• 0.998

• 1.503

Multiple Choice

What is the line of best fit?

• f(x)= 5x+1.82
• cannot be determined
• f(x)= 1.82x + 5.02
• f(x)= 1.1x + 4.2