Question

The number of wins for a high school football team is measured for the season. When the team plays at home, it is generally believed that they will win. Comparing the location of the game and the number of wins, a correlation coefficient of −0.11 is calculated. What would this imply about the football team winning at home?
A. The scatter plot would closely resemble a straight line with a negative slope. The data has a strong, negative correlation, and a causal relationship exists between the team playing at home and winning.
B. The scatter plot would closely resemble a straight line with a negative slope. The data has a strong, negative correlation, but causation cannot be determined.
C. The scatter plot would not be represented by a line of best fit with a negative slope. There is a weak correlation between the football team playing at home and winning, and a causal relationship exists between the team playing at home and winning.
D. There is no causation and almost no correlation between the football team playing at home and winning.

Answer 1

Answer:

• D. There is no causation and almost no correlation between the football team playing at home and winning.

Explanation:

The correlation coefficient is a measure of how strength is the relationship between two random variables. This measure quanitifes to what extent two random variables are associated or correlated.

The correlation coefficient can take values from - 1 to + 1.

A correlation coefficient of - 1 means a perfect, negative, linear linear correlation.

A correlation coefficient of + 1 means a perfect, positive, linear correlation.

A correlation coefficient of 0 means that the variables cannot be linearly correlated at all.

For intermediates values of the correlation coefficient, the variables are somewhat linearly correlated; the closer to ± 1 the stronger the correlation, the closer to 0, the weaker the correlation.

A correlatons coefficient of  - 0.11 is pretty close to zero, meaning that the two variables, "the location of the game" and "the number of wins" are almost not correlated. Of course, much less could you think about a causation relationship between them.

Answer 2

Answer:

D. There is no causation and almost no correlation between the football team playing at home and winning.