Lesson on Correlation

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Multiple Choice

Which example shows CORRELATION? (The events show correlation, but one thing does NOT cause the other thing to happen.)

• I put water in the freezer and now I have ice.

• The alarm clock went off and I woke up.

• Temperature and the amount of people at the beach.

Multiple Choice

Which one of these examples is NOT an example of CAUSATION?

• Kryptonite causes Superman to lose all his powers.

• Temperatures of less than 32˚F cause water to freeze.

• Umbrellas cause rainstorms.

• Stepping on the gas pedal causes a car to move faster.

Multiple Choice

Which example shows CAUSATION? (Which one CAUSED the other to happen.)

• Rainfall and time spent reading.

• Eating more butter and increased divorce rates.

• It started raining and the baseball game was delayed.

Multiple Choice

Which example shows CAUSATION? (Which one CAUSED the other to happen.)

• High social media usage and reduced grades.

• Car ran out of gas and being stranded on the side of the road.

• Recess time and number of friends.

Types of Correlation

• Positive

• Negative

• No Correlation

R

Tells us the strength of the relationship/correlation

--> Closer to 1 or -1, the stronger the relationship

​

Correlation Coefficient

​Negative Correlation

​

​Positive Correlation

No Correlation

The closer to 0, the weaker the correlation. Very close to 0 is no correlation. The closer to -1 or 1, the stronger the correlation. -1 and 1 are perfect.

Multiple Choice

Make a prediction for a resting heart rate after 6 hours of exercise a week.

• 6
• 50
• 55
• 59

Multiple Choice

If Joe worked 30 hours, how much is he expected to earn?

• $600
• $200
• $1000
• $800

Multiple Choice

Write the linear regression equation for the following data points. Round to the nearest hundredth.

• $$y=-0.83x+0.61$$

• $$y=-0.83x+0.63$$

• $$y=0.83x+-0.8$$

• y = -0.828767x + 0.609589

Multiple Choice

Exit Ticket: What is the correlation coefficient and linear regression of the data set: (1,7) (2,4) (3,-1) (8,-9) (6,-3) (-1,10).

• r = .98 & y = 7.9x - 2.1

• r = .97 & y = 7.9x - 2.1

• r = .95 & y = 7.9x - 2.1

• r = .98 & y = -2.1x + 7.9

• r = .97 & y = -2.1x + 7.9

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

Multiple Choice

Using your linear regression, what is y when x is 30?

• 61.59
• 52.46
• 57.94
• 59.76

Multiple Choice

The linear regression equation is y = 61.93x - 1.79.  According to the model, the slope can be interpreted as:

• After 0 hours of driving, they went 61.93 miles.
• They drove at a speed of 61.93 miles per hour.
• They drove 61.93 miles total.
• They drove 61.93 hours total.

Multiple Choice

Describe the relationship between the variables.

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

Multiple Choice

Which correlation coefficient (r) best represents the graph?

• r = -1

• r = 0

• r = 1.4

• r = 1

Multiple Choice

Which correlation coefficient (r) best represents the graph?

• r = -0.95

• r = 0

• r = 0.85

• r = 1.1

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

C) What does the correlation coefficient tell you about the number of hours each student is watching TV per week and their IQ?

• Strong Negative Correlation

• Weak Negative Correlation

• No Correlation

• Weak Positive Correlation

• Strong Positive Correlation

Multiple Choice

Which relationship is shown by this scatter plot?

• As the cost goes down, the number sold goes down

• As the cost goes up, the number sold goes down.

• As the cost does down, the number sold remains the same

• There is no relationship between cost and the number sold.

Multiple Choice

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

• A
• B
• C
• D

Multiple Choice

The table shown is comparing a person's foot length to their height in cm. Calculate a line of best fit.

• f(x) = 25.05x + 5.57

• f(x) = 5.57x + 25.05

• f(x) = -5.57x + 25.05

• f(x) = 5.57x - 25.05

Multiple Choice

A person travels by car. They record their miles driven in a data table. Calculate the linear regression equation of this data.

• y = 61.93x - 1.79

• y = -1.79x + 61.93

• y = 0.016x + 0.03

• y = 0.03x + 0.016

Multiple Choice

What is the regression line?

• f(x)= 5x+1.82

• cannot be determined

• f(x)= 1.82x + 5.02

• f(x)= 1.1x + 4.2

Write the equation of the line.