Correlation and Causal Relationships

What type of relationship exists between the number of pages printed on a printer and the amount of ink used by that printer?

• Positive correlation, but not causal

• Positive correlation, and causal

• Negative correlation, but not causal

• Negative correlation, and causal

Which situation does not describe a causal relationship?

• The higher the volume on a radio, the louder the sound will be.

• The faster a student types a research paper, the more pages it will have.

• The shorter the distance driven, the less gasoline will be used.

• The slower the pace of a runner, the longer it will take the runner to finish the race.

The data obtained from a random sample of track athletes showed that as foot size of the athlete decreased, the average running peed decreased. Which statement is best supported by the data?

• Smaller foot sizes cause track athletes to run slower.

• The sample of track athletes shows a causal relationship between foot size and running speed.

• The sample of track athletes shows a correlation between foot size and running speed.

• There is no correlation between foot size and running speed in track athletes.

The table above shows 6 students' overall averages and their averages in math class. If a linear model is applied to the to these data, which statement best describes the correlation coefficient?

• It is close to -1.

• It is close to 1.

• It is close to 0.

• It is close to 0.5.

The scatterplot above compares the number of bags of popcorn and the number of sodas sold at each performance of the circus over one week. Which conclusion can be drawn from the scatterplot?

• There is a negative correlation between popcorn sales and soda sales.

• There is a positive correlation between popcorn sales and soda sales.

• There is no correlation between popcorn sales and soda sales.

• Buying popcorn causes people to buy soda.

What is the correlation coefficient of the linear fit of the data shown above, to the nearest hundredth?

• 1.00

• 0.93

• -0.93

• -1.00

Bella recorded data and used her graphing calculator to find the equation for the line of best fit. She then used the correlation coefficient to determine the strength of the linear fit. Which correlation coefficient represents the strongest linear relationship?

• 0.9

• 0.5

• -0.3

• -0.8

Analysis of data from a statistical study shows a linear relationship in the data with a correlation coefficient of -0.524. Which statement best summarizes the result?

• There is a strong positive correlation between the variables.

• There is a strong negative correlation between the variables.

• There is a moderate positive correlation between the variables.

• There is a moderate negative correlation between the variables.

The results of a linear regression are shown above. Which phrase best describes the relationship between x and y?

• Strong negative correlation

• Strong positive correlation

• Weak negative correlation

• Weak positive correlation