Scatter Plots and Trend Lines

Scatter Plots and Trend Lines

Vocabulary

• Scatter Plot: Used to show the relationship between two sets of data

• Positive Association (Correlation): Both variables are increasing

• Negative Association (Correlation): One variable (x) increases, while the other (y) decreases

• No Association (Correlation): The variables are not related in any way

Multiple Choice

The amount of items you buy and the amount of money left in your wallet is an example of...

• Positive Association

• Negative Association

• No Association

Multiple Choice

The number of times you brush your teeth in one week and the number of cars in the United States is an example of...

• No Association

• Positive Association

• Negative Association

Open Ended

Is this trend line a good fit? Why or why not?

Open Ended

Is this trend line a good fit? Why or why not?

Open Ended

Is this trend line a good fit? Why or why not?

A good trend line

will help us make predictions. If we want to know an approximate cost per gallon of gas 10 years after 1970 (1980), we can use a trend line to help us!

If we travel out to 10 on the years (x) axis, we can then travel up to the trend line to make our prediction!

In 1980, the average cost of gas was $.75 per gallon! That's crazy!

It's important to note...

we want our prediction to be as close to the trend line as possible! It may not always be right on the line, but the closer we are to the trend line, the bettre the prediction is!

YOUR TURN!

Make a prediction based on the trend lines!

Open Ended

If x=10, what is a reasonable prediction for the value of y?

Open Ended

If y=225, what is a reasonable prediction for the value of x?

Multiple Choice

If x=5, what is a reasonable prediction for the value of y?

• 170

• 225

• 100

• 150

Trend Line Equations

While estimating visually with trend lines is helpful, there are also times when the equation of the trend line can be useful, especially when predicting a value that CANNOT be seen on the graph.

Let's look at some trend lines

and find their equations!

Let's start with the y-intercept (b)!

What is the y-intercept of this trend line?

Now let's find the slope!

By picking "smart points" and using our Rise (red) and our Run (blue) method, we can see that we have a rise of -2 and a run of 6. We can now make the ratio of

 $\frac{RISE}{RUN}=\frac{-2}{\ \ 6}=\frac{-1}{\ \ 3}$  

and we have our slope (m)!

Multiple Choice

If our y-intercept is 8 and our slope is 

 $\frac{-1}{\ \ 3}$  , then the equation for our trend line is....

•  $y=-8x+\frac{-1}{\ \ 3}$  
  

•  $y=\frac{1}{3}x-8$  
  

•  $y=\frac{-1}{\ \ \ 3}x+8$  

•  $y=8x-\frac{1}{3}$  

YOUR TURN!

Try to come the equations for the following trend lines!

Open Ended

What is the y-intercept of this line?

Open Ended

What is the slope of this line?

Open Ended

What is the equation for this trend line?

Multiple Choice

What is the equation for the trend line shown?

• $y=\frac{2}{3}x+40$

• $y=40x$

• $y=\frac{2}{3}x$

• $y=\frac{20}{3}x+40$

Ok let's see what you remember!

Multiple Choice

What is the type of correlation for the following scatter plot?

• Negative

• None

• Positive

Multiple Choice

What type of association does this graph have?

• positive
• negative
• none
• all of the above

Multiple Choice

Write an equation for the trend line

• y= 0.5x

• y= 2x

• y= -0.5x

• y= -2x

Multiple Choice

What is a line of best fit used for?

• To make predictions
• To make the graph look pretty
• To connect the points

Multiple Choice

If a scatterplot has no correlation then...

• ...it has no ordered pairs
• ...it has ordered pairs that have a negative pattern
• ...its ordered pairs have no predictable pattern
• ...if it makes a lion on a graph (roar!)

Multiple Choice

the slope is -5/7, what does that mean?

• gain 5 hour of sleep for 7 cups of coffee
• lose 5 hours of sleep for 7 cups of coffee
• lose 7 cups of coffee for 5 hours of sleep
• lose 5 cups of coffee for 7 hours of sleep

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 pages would be in a book with 6 chapters. 

• ≅100 pages
• ≅170 pages
• ≅60 pages
• ≅20 pages