Question

lesson 7: the correlation coefficient
cool down: what is a correlation coefficient?

1. what information does a correlation coefficient tell you about the data in a scatter

plot?

1. which value best estimates the value for the correlation coefficient of the scatter

plot: -1, -0.8, -0.2, 0.2, 0.8, or 1? explain your reasoning.

Explanation:

1. A correlation coefficient tells you two things:

• Direction: If it is positive, there is a positive linear relationship (as one variable increases, the other tends to increase). If it is negative, there is a negative linear relationship (as one variable increases, the other tends to decrease).
• Strength: The closer the absolute value of the correlation coefficient is to 1, the stronger the linear relationship. A value of 0 indicates no linear relationship.

1. Looking at the scatter - plot:

• The points show a negative trend (as \(x\) increases, \(y\) decreases), so the correlation coefficient is negative.
• The points are somewhat close to the line of best - fit (not perfectly on the line, so it's not - 1). A value of - 0.2 would imply a very weak negative relationship, but the points in the scatter - plot seem to follow the negative trend more closely than a weak relationship. So, the value that best estimates the correlation coefficient is - 0.8.

Answer:

1. A correlation coefficient tells the direction (positive or negative) and strength (how close to - 1 or 1) of the linear relationship between two variables in a scatter plot.
2. - 0.8. The scatter - plot shows a negative trend (so negative value) and the points are relatively close to the line of best - fit (so closer to - 1 than - 0.2).