Question
x-Value y-Value
1
23
5
27
7
32
11
35
15
39
43
17
Find the correlation coefficient of the data using technology (such as GeoGebra). Round your r- value to two decimal places, if necessary.
1
23
5
27
7
32
11
35
15
39
43
17
Find the correlation coefficient of the data using technology (such as GeoGebra). Round your r- value to two decimal places, if necessary.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the correlation coefficient \( r \) for the given data, we can use technology, but I can guide you through the steps to calculate it manually or use an online tool like GeoGebra.
Your data points look like this:
\[
\begin{align*}
x & : 1, 5, 7, 11, 15, 17, 23, 27, 32, 35, 39, 43 \\
y & : 1, 23, 27, 32, 35, 39, 43 \\
\end{align*}
\]
First, we'll calculate the needed statistics to find \( r \):
1. Calculate the means of \( x \) and \( y \).
2. Compute the necessary sums to find \( r \):
- \( \sum x \)
- \( \sum y \)
- \( \sum xy \)
- \( \sum x^2 \)
- \( \sum y^2 \)
3. Use the formula for the correlation coefficient \( r \):
\[
r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}
\]
Where \( n \) is the number of data points.
### Input Data
- \( x \): 1, 5, 7, 11, 15, 17, 23, 27, 32, 35, 39, 43
- \( y \): 1, 23, 27, 32, 35, 39, 43 (This seems to have mixed values in your input; ensure y-values correspond properly to x-values.)
### Manual Calculation
1. Find the mean \( \overline{x} \) and \( \overline{y} \).
2. Compute necessary sums:
- Calculate \( n = 12 \)
- Calculate \( \sum x = 1 + 5 + 7 + 11 + 15 + 17 + 23 + 27 + 32 + 35 + 39 + 43 \)
- Calculate \( \sum y = 1 + 23 + 27 + 32 + 35 + 39 + 43 \)
- Continue for the other sums.
This is an example of how you can approach the calculation.
If you have access to a statistical tool like GeoGebra, enter your data pairs, and it should calculate the correlation coefficient for you.
### Correlation Coefficient (from technology)
Once you’ve input the data correctly, the output should give you the \( r \) value.
Usually, the result from a computational tool would give you results rounded to two decimal places. For a perfect understanding, please double-check in the specific tool or environment you are using.
If you get \( r = \) some value, round it accordingly to two decimal places.
If you have access to GeoGebra or any statistical software, please enter your complete data to get the correlation correctly.
Your data points look like this:
\[
\begin{align*}
x & : 1, 5, 7, 11, 15, 17, 23, 27, 32, 35, 39, 43 \\
y & : 1, 23, 27, 32, 35, 39, 43 \\
\end{align*}
\]
First, we'll calculate the needed statistics to find \( r \):
1. Calculate the means of \( x \) and \( y \).
2. Compute the necessary sums to find \( r \):
- \( \sum x \)
- \( \sum y \)
- \( \sum xy \)
- \( \sum x^2 \)
- \( \sum y^2 \)
3. Use the formula for the correlation coefficient \( r \):
\[
r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}
\]
Where \( n \) is the number of data points.
### Input Data
- \( x \): 1, 5, 7, 11, 15, 17, 23, 27, 32, 35, 39, 43
- \( y \): 1, 23, 27, 32, 35, 39, 43 (This seems to have mixed values in your input; ensure y-values correspond properly to x-values.)
### Manual Calculation
1. Find the mean \( \overline{x} \) and \( \overline{y} \).
2. Compute necessary sums:
- Calculate \( n = 12 \)
- Calculate \( \sum x = 1 + 5 + 7 + 11 + 15 + 17 + 23 + 27 + 32 + 35 + 39 + 43 \)
- Calculate \( \sum y = 1 + 23 + 27 + 32 + 35 + 39 + 43 \)
- Continue for the other sums.
This is an example of how you can approach the calculation.
If you have access to a statistical tool like GeoGebra, enter your data pairs, and it should calculate the correlation coefficient for you.
### Correlation Coefficient (from technology)
Once you’ve input the data correctly, the output should give you the \( r \) value.
Usually, the result from a computational tool would give you results rounded to two decimal places. For a perfect understanding, please double-check in the specific tool or environment you are using.
If you get \( r = \) some value, round it accordingly to two decimal places.
If you have access to GeoGebra or any statistical software, please enter your complete data to get the correlation correctly.
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