To analyze the given data, let's break it down step by step.
Part A: Calculate the Correlation Coefficient (r-value)
To find the correlation coefficient (r-value), you would typically input the data into a statistical calculator, spreadsheet software, or use a tool like Desmos as mentioned. The formula for r can be derived from:
\[ r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n \sum x^2 - (\sum x)^2][n \sum y^2 - (\sum y)^2]}} \]
Where:
- \(n\) = number of data points
- \(\sum xy\) = the sum of the product of each x and y
- \(\sum x\) = the sum of all x values
- \(\sum y\) = the sum of all y values
- \(\sum x^2\) = the sum of all x values squared
- \(\sum y^2\) = the sum of all y values squared
Let's compute these summations:
- \( \sum x = 55 \) (1+2+3+4+5+6+7+8+9+10)
- \( \sum y = 475 \) (29+34+37+40+42+44+47+52+55+60)
- \( \sum xy = 2851 \) (1×29 + 2×34 + ... + 10×60)
- \( \sum x^2 = 385 \) (1^2 + 2^2 + ... + 10^2)
- \( \sum y^2 = 22025 \) (29^2 + 34^2 + ... + 60^2)
- \( n = 10 \)
Using these values, we can input them into the correlation formula to find that \( r \approx 0.993 \).
Part A Answer
\( r \approx 0.993 \)
Part B: Implication of the r-value
Since the r-value is positive, it implies that there is a positive correlation.
Part B Answer
The r-value implies that this data has a positive correlation.
Part C: Strength of the Correlation
An r-value close to +1 or -1 (typically above 0.7 or below -0.7) is considered a strong correlation. Since \( r = 0.993 \), this indicates a strong positive correlation.
Part C Answer
The strength of this correlation is strong.
1 answer