
or
Find the correlation coefficient, r, of the data described below.
Bernie is indignant that his favorite author takes too long to write new books. To determine how atypical his favorite author's speed is, Bernie looked at how writing speed varies between different active authors.
For his favorite novelists, he recorded the number of years they had been actively writing, x, and how many novels they had written, y.
Years	Novels
6	7
25	10
26	14
29	14
32	20
Round your answer to the nearest thousandth.


To calculate the correlation coefficient \( r \), we can use the formula for Pearson's correlation coefficient:

\[
r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}
\]

Where:
- \( n \) is the number of data points,
- \( x \) represents the years,
- \( y \) represents the number of novels,
- \( \sum x \) is the sum of the \( x \)-values,
- \( \sum y \) is the sum of the \( y \)-values,
- \( \sum xy \) is the sum of the products of corresponding \( x \) and \( y \)-values,
- \( \sum x^2 \) is the sum of the squares of the \( x \)-values, and
- \( \sum y^2 \) is the sum of the squares of the \( y \)-values.

Let's calculate these values step by step.

Given data points:

\[
x: 6, 25, 26, 29, 32
\]
\[
y: 7, 10, 14, 14, 20
\]

I'll calculate each term and then solve for \( r \).The correlation coefficient \( r \) for the given data is approximately \( 0.839 \), rounded to the nearest thousandth.

Would you like a more detailed explanation, or do you have any further questions?

Here are five related questions for further exploration:
1. How do you interpret a correlation coefficient of 0.839 in this context?
2. What are the limitations of using the Pearson correlation coefficient in analyzing data?
3. How would you calculate the line of best fit for this data?
4. How does the correlation coefficient help in predicting trends between the variables?
5. What are alternative methods to measure the relationship between variables?

**Tip:** A correlation coefficient close to 1 implies a strong positive linear relationship between the variables.

Find the correlation coefficient, r, of the data described below. Bernie is indignant that his favorite author takes too long to write new books. To determine how atypical his favorite author's speed is, Bernie looked at how writing speed varies between different active authors. For his favorite novelists, he recorded the number of years they had been actively writing, x, and how many novels they had written, y. Years: 6, 25, 26, 29, 32. Novels: 7, 10, 14, 14, 20. Round your answer to the nearest thousandth.

Calculate the correlation coefficient (r) for the number of years active and the number of novels written by various authors. This problem uses the Pearson correlation coefficient formula and is suitable for high school students (Grades 10-12). Data points include years (6, 25, 26, 29, 32) and novels (7, 10, 14, 14, 20).

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