Linear of Best Fit

Multiple Choice

What does correlation mean?

• I have a bf/gf

• is a potential relationship between two variables

• it grows at the bottom of the ocean

• is a graph that has points scattered all arounf it

Multiple Choice

Describe this scatter plot

• It has a strong negative correlation

• it has a weak positive correlation

• no correlation

• It has a strong positive correlation

Multiple Choice

Describe this scatter plot

• weak postive correlation

• weak negative correlation

• no correlation

• ham and cheese

Scatter Plots can be described as linear and non-linear models. They are not perfectly linear or non-linear but they​ follow a trend.

Linear vs. Non-linear Models

​

Multiple Choice

Which scatter plot shows a linear relationship between x and y?

• Graph A

• Graph B

• Graph C

• Graph D

What is our goal for the day?

Students will learn to find & draw the line of best fit.
Students will use the line of best fit to make predictions

Some text here about the topic of discussion

Scatter Plots: Line of Best Fit

1. ​To create the line of best fit, you must draw a STRAIGHT line that passes through the middle of your graph. You must have the same number of dots above and below the line.

2. Your line does NOT have to pass through ALL your dots. It doesn't have to pass through ANY dots.

​Let's Practice

Multiple Choice

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

• A
• B
• C
• D

Multiple Choice

Which line is the best line of best fit?

• a

• b

• c

• i don't see any lines

Multiple Choice

Is this line an accurate line estimate of best fit for the data?

• Yes

• No

Writing an equation for the line of best fit.

• Find the y intercept It is your b.

      

  
  

• Find the slope. It is your m.

  
  

• Plug it into y =mx + b

  
  

• b = 7

• m = -4/7

• y = -4/7x + 7

• Now predict what happens when x = 7, what does y =?

Multiple Choice

The graph shows a line of best fit for data collected on the amount of income earned by lawn companies in relation to the number of yards mowed.  What is the equation of the line of best fit?

• y = (3/2) x
• y = 30x
• y = 30x + 300
• y = (3/2)x + 300

Multiple Choice

The graph shows a line of best fit for data collected on the price of a unit in relation to the number of units sold.  What is the equation of the line of best fit?

• y = - (1/2) x + 10
• y = - (1/50) x + 40
• y = - (1/2) x + 40
• y = - (1/50) x + 10

Multiple Choice

The graph above shows a line of best fit for data collected on the distance bicyclists have remaining in relation to the amount of time they have been riding.  What is the equation of the line of best fit?

• y = -25x + 170
• y = 25x + 170
• y = -(5/8) x + 170
• y = (5/8) x + 170

Multiple Choice

which scatterplot shows the correct trend line (line of best fit) for the relationship showing the number of bags of chocolates that are sold and the price per bag?

• A

• B

• C

• D

Multiple Choice

Is this line an accurate line estimate of best fit for the data?

• Yes

• No

Multiple Choice

which scatterplot shows the correct trend line (line of best fit) for the relationship showing the number games played and attendance in the Small Fry Baseball Tournament?

• W

• X

• Y

• Z

Line of Best Fit

• line through a scatter plot of data points that best expresses the relationship between those points. 

• can use the line of best fit to predict what could happen

• The line of best fit should be in the middle of the points

​2 Ways to predict

​Interpolation is the process of making a prediction within the given data set.

​Extrapolation is the process of making a prediction outside of the given data set.

Using Line of Best Fit to Make Predictions

• Based on the line of best fit

• how many points did someone who player 8 minutes score?

Multiple Choice

What is a line of best fit used for?

• To make predictions
• To make the graph look pretty
• To connect the points
• To make it look like you know what you are doing

Multiple Choice

The scatter plot shows the relationship between the number of chapters and the total number of pages for several books.  Use the trend line to predict how many chapters would be in a book with 180 pages. 

• 12 chapters
• 15 chapters
• 18 chapters
• 21 chapters

Multiple Choice

A small theme park is trying to determine the number of guests they should expect on a weekend, based on the temperature outside.  Based on the trend line, about how many guests should be expected if the temperature is around 80°?

• 8,300
• 8
• 7,300
• 9,300

Multiple Choice

A teacher made the following graph showing absences vs. final grades. Predict the grade of a student that has 7 absences.

• 50

• 45

• 70

• 60

Multiple Choice

A small theme park is trying to determine the number of guests they should expect on a weekend, based on the temperature outside. Based on the trend line, about how many guests should be expected if the temperature is around 80°?

• 8000

• 8500

• 7300

• 9300

Multiple Choice

The graph below shows a line of best fit for data collected on the amount of time teenagers spend on the computer and watching television.

Based on the line of best fit, how much time does a teenager spend watching television if they spend 120 minutes on the computer?

• 150 min

• 135 min

• 165 min

• 180 min