The correlation coefficient of the health research institute data measures the relationship between the age and the years of the smokers
The correlation coefficient is 0.53
<h3>How to calculate the correlation coefficient</h3>
The correlation coefficient (r) is calculated as:
![r = \frac{n(\sum xy) - \sum x \sum y}{\sqrt{[n \sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2}}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7Bn%28%5Csum%20xy%29%20-%20%5Csum%20x%20%5Csum%20y%7D%7B%5Csqrt%7B%5Bn%20%5Csum%20x%5E2%20-%20%28%5Csum%20x%29%5E2%5D%5Bn%5Csum%20y%5E2%20-%20%28%5Csum%20y%29%5E2%7D%7D)
Using the given parameters, we have:
![r = \frac{20 *8249 - 1257* 116}{\sqrt{[20 * 98823 - 1257^2][20 * 836 - 116^2}}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B20%20%2A8249%20-%201257%2A%20116%7D%7B%5Csqrt%7B%5B20%20%2A%2098823%20-%201257%5E2%5D%5B20%20%2A%20836%20-%20116%5E2%7D%7D)
Evaluate the exponents
![r = \frac{20 *8249 - 1257* 116}{\sqrt{[20 * 98823 - 1580049][20 * 836 - 13456}}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B20%20%2A8249%20-%201257%2A%20116%7D%7B%5Csqrt%7B%5B20%20%2A%2098823%20-%201580049%5D%5B20%20%2A%20836%20-%2013456%7D%7D)
Evaluate the products
![r = \frac{164980 - 145812}{\sqrt{[1976460 - 1580049][16720 - 13456}}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B164980%20-%20145812%7D%7B%5Csqrt%7B%5B1976460%20-%201580049%5D%5B16720%20-%2013456%7D%7D)
Evaluate the differences
Evaluate the product
Evaluate the root
Evaluate the quotient
Hence, the correlation coefficient is 0.53
Read more about correlation coefficient at:
brainly.com/question/1564293
Her best choice would be to take a fixed rate mortgage because it would let her know exactly how much she would pay each month.
40% = 32/x
Rewrite using a decimal
.40 = 32 / x
Multiply both sides by x
.40x = 32
Divide both sides by .40
x = 32 / .40
x = 80
Write the full fraction
32/80
Answer 32/80
The graph is attached below.
In order to find the y-intercept, check the graph and see where it hits the y-axis, so in this case the y-intercept would be at (0,6).
To find the x-intercept, check the graph and see where it hits the x-axis, and here it hits at x = -6.
