Question

name:
algebra cc
date:
standards: a.dsr.10.7 distinguish between correlation and causation. a.dsr.10.3 represent data on two quantitative variables on a scatter plot and describe how the variables are related. a.dsr.10.4 interpret the slope (predicted rate of change) and the intercept (constant term) of a linear model based on the investigation of the data.
learning target: i can create a line fitted to data that shows a linear correlation and use it to make predictions.
engage
what is an example of bivariate data that would have a correlation coefficient ( r = 1 )?
what about an example of data that might have a correlation coefficient of ( r = 0 )?

Explanation:

A correlation coefficient \( r = 1 \) indicates a perfect positive linear relationship. An example of bivariate data with \( r = 1 \) could be the number of hours studied and the corresponding increase in test scores (assuming a perfect linear increase). A correlation coefficient \( r = 0 \) indicates no linear relationship. An example could be the number of books read and shoe size (as there is no inherent linear connection between these two variables).

Answer:

• For \( r = 1 \): Number of hours studied and test scores (assuming a perfect linear increase).
• For \( r = 0 \): Number of books read and shoe size.