Scatter Plots, Linear Regression, Correlation Coefficient

Scatter Plots, Linear Regression, Correlation Coefficient

By Shalynne Orth

Multiple Choice

What type of association does this graph have?

• positive

• negative

• none

• all of the above

Multiple Choice

What type of association does this graph have?

• positive 
• negative
• none
• all of the above

Multiple Choice

What is the correlation?

• Negative correlation

• No correlation

• Positive correlation

• All of the above

Multiple Choice

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

• Graph A
• Graph B
• Graph C
• Graph D

Multiple Choice

In a scatterplot, an outlier...

• ...is something we didn't learn 8th grade
• ...is a puppet with a long nose named Pinocchio
• ...is a point that is far outside the main cluster of points/ordered pairs
• ...is a really naughty point who doesn't tell the truth when outside

Multiple Choice

As the age of the car increases, its value decreases. Which scatterplot represents this relationship?

• A
• B
• C
• D

Why linear regression?

Use linear regression to predict the outcome of a progression using a given set of data.

​

We do this by finding the line of best fit for a set of data points.​

​

Multiple Choice

What is a best-fit line 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

If x is temperature and y is coffee sales, use the following formula to determine the coffee sales on a 34° day.

y = -60x+6443

• $4403

• $4673

• $8483

• $6443

How to find a linear regression equation:

• Enter the table of values into desmos

• On the next line, type EXACTLY this: y_1~mx_1+b

• Desmos will tell the value of m and b!

​Find the linear regression equation for the data set:

1. Click the plus sign on www.desmos.com

2. Click "table"

3. Enter the values​

4. On the next line​ under the table, type y_1=mx_1+b

5. Desmos will give you m and b. Plug them into y=mx+b to get your equation! 

^Equation is y=3x-1

Multiple Choice

Write the equation for the linear regression shown.

• $$y=-5.11x+3.23$$

• $$r=0.8$$

• $$y=3.23x\ -\ 5.11$$ $$\$$

• $$y=0.64x+0.8$$

Multiple Choice

A restaurant sells pizza for the prices in the data table. Calculate the linear regression equation of the data.

• y = 1.5x + 12

• y = 12x + 1.5

• y = 0.67x - 8

• y = -8x + 0.67

Multiple Choice

The chart below tracts starting salaries for health care workers since the year 2000. Using linear regression, find the equation of best fit. Round decimals to 3 places.

• y = 839.721x + 27541.812
• y = 27541.812x - 839.721
• y = 27541.812x + 839.721
• y = 839.721x - 27541.812

So...What is the r value that desmos gives us?

The r value means correlation coefficient. It tells us how well the line of best fit actually fits the data.

​​r will be a number between -1 and 1

• If r>0, it's POSITIVE correlation.

• If r<0, it's NEGATIVE correlation.​

• If r is closer to 1 or -1, it's STRONG correlation (fits really well!)

• If r is closer to 0, it's WEAK correlation​ (does not fit well)

​​In the example we did previously, r=1. (Don't worry about r^2.)

​

This means the line of best fit is a PERFECT fit. (It touches every single points right through the middle).​

​

Study Time and Grades

As study hours increase, grades increase. There is a positive correlation between hours and grades.

So....Do hours spent studying cause higher grades? Likely, yes!

Multiple Choice

Estimate the correlation coefficient for this scatterplot.

• A) r = 1.2

• B) r = 0.89

• C)r = 0

• D) r = -0.89

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

As x increases, y increases

• A) correlation coefficient

• B) causation

• C) positive correlation

• D) negative correlation

Multiple Choice

As x increases, y decreases.

• A) no correlation

• B) negative correlation

• C) correlation coefficient

• D) positive correlation

Multiple Choice

Average fat intake per citizen of a country and average cancer rate of a country.  $$r=.73$$  

• strong positive

• strong negative

• weak positive

• weak negative

Multiple Choice

Temperature of a rubber band and distance the rubber band can stretch. $$r=.84$$  

• strong positive

• strong negative

• weak positive

• weak negative

Multiple Choice

Score on science exam and number of words written on the essay question.  $$r=.28$$  

• strong positive

• strong negative

• weak positive

• weak negative

Multiple Choice

Average time spent listening to music per day and average time spent watching TV per day.  $$r=-.17$$  

• strong positive

• strong negative

• weak positive

• weak negative