Multiple Choice
Which of the following tables shows a negative correlation between variables and ?
59
views
11. Correlation
Correlation Coefficient
Multiple Choice
Given the following pairs of data: , , and , which of the following values could represent the correlation coefficient between the and variables?
A
B
C
D
Verified step by step guidance1
Step 1: Understand that the correlation coefficient measures the strength and direction of a linear relationship between two variables, ranging from -1 to 1.
Step 2: Identify the given data points: (1, 1), (-1, 5), and (10, y), where y is unknown. The goal is to find a value of y that could produce a correlation coefficient close to the given options.
Step 3: Recall the formula for the Pearson correlation coefficient \(r\):
\[r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}}\]
where \(\bar{x}\) and \(\bar{y}\) are the means of the x and y values respectively.
Step 4: Calculate the means \(\bar{x}\) and \(\bar{y}\) using the three x-values (1, -1, 10) and the three y-values (1, 5, y). Express \(\bar{y}\) in terms of y.
Step 5: Substitute the values into the correlation formula and solve for y such that the correlation coefficient \(r\) is approximately 0.8, verifying that this value is possible given the data.
Related Videos
Related Practice
