Question

Baruch College has 1000 students in the spring of 2021. 30 percent of the students use the gym twice per week, and 70 percent of the students use the gym three times per week. Which measure tells us the strength of the linear relationship between X and Y? The measure that tells us the strength of the linear relationship between X and Y is 2. Correlation coefficient," often denoted as r. It measures the degree and direction of a linear relationship between two variables.

Answer 1

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables, ranging from -1 to +1. The coefficient of determination (r²) expresses what portion of variability in one variable is explained by the other. Correlation does not necessarily mean causation.

Step-by-step explanation:

The correlation coefficient, denoted as r, is essential for measuring the strength and direction of the linear relationship between two variables. If we have variables X and Y, and we suspect they might be related linearly, r can accurately quantify the degree of their association. The value of r ranges from -1 to +1, where a value close to +1 indicates a strong positive relationship, a value close to -1 indicates a strong negative relationship, and a value close to 0 suggests a weak or no linear relationship.

The coefficient of determination, represented by r², is the square of the correlation coefficient. This statistical measure explains, when converted to a percentage, how much of the variability in the dependent variable Y can be accounted for by the variability in the independent variable X using the regression line. For example, an r² of 0.44 implies that approximately 44 percent of the variation in Y can be explained by X.

It's also important to note that the correlation coefficient itself does not imply causation. While it indicates the strength of the relationship, to establish causation, one would need to conduct specific experiments.