The graph below plots the values of y for different values of x:
Plot the ordered pairs 1, 3 and 2, 4 and 3, 9 and 4, 7 and 5, 2 and 6,18
Which correlation coefficient best matches the data plotted on the graph?
0.5
0.8
0.9
1.0
pls help me
0.9
I'm working on the same problem! I need help!
The answer is 0.5, I just took the test
To determine which correlation coefficient best matches the data plotted on the graph, we need to understand what a correlation coefficient is and how it relates to the data.
A correlation coefficient is a statistical measure that represents the strength and direction of the relationship between two variables. It ranges from -1 to 1. A positive correlation coefficient (between 0 and 1) indicates a positive relationship, meaning that as one variable increases, the other variable also tends to increase. A negative correlation coefficient (between -1 and 0) indicates a negative relationship, meaning that as one variable increases, the other variable tends to decrease.
To find the correlation coefficient, we can use the standard formula:
r = (N * ΣXY - ΣX * ΣY) / √((N * ΣX^2 - (ΣX)^2) * (N * ΣY^2 - (ΣY)^2))
Here:
- N is the number of data points (in this case, the number of ordered pairs)
- ΣXY is the sum of the products of the corresponding x and y values
- ΣX is the sum of all x values
- ΣY is the sum of all y values
- ΣX^2 is the sum of the square of all x values
- ΣY^2 is the sum of the square of all y values
Now, let's calculate the correlation coefficient for the given data points:
Ordered pairs: (1, 3), (2, 4), (3, 9), (4, 7), (5, 2), (6,18)
Step 1: Calculate necessary sums:
ΣX = 1 + 2 + 3 + 4 + 5 + 6 = 21
ΣY = 3 + 4 + 9 + 7 + 2 + 18 = 43
ΣX^2 = 1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 = 91
ΣY^2 = 3^2 + 4^2 + 9^2 + 7^2 + 2^2 + 18^2 = 469
ΣXY = (1*3) + (2*4) + (3*9) + (4*7) + (5*2) + (6*18) = 291
N = 6
Step 2: Plug the values into the formula:
r = (N * ΣXY - ΣX * ΣY) / √((N * ΣX^2 - (ΣX)^2) * (N * ΣY^2 - (ΣY)^2))
r = (6 * 291 - 21 * 43) / √((6 * 91 - (21)^2) * (6 * 469 - (43)^2))
r = 1758 - 903 / √((546 - 441) * (2814 - 1849))
r = 855 / √(105 * 965)
r ≈ 0.782
Based on the calculation, the correlation coefficient for the given data is approximately 0.782. Comparing this to the given options, the correlation coefficient that best matches this value is 0.8.