Answer:
r=0.96
Step-by-step explanation:
The Pearson product-moment correlation coefficient (PMCC) is a numerical value between -1 and 1 that shows the strength of the linear relationship between two variables.
Given the result of 10 hospital patients which were sampled below:
![\left|\begin{array}{c|ccccccccccccc}$Patient&A&B&C&D&E&F&G&H&I&J\\$Age (X) in Years&20&25&50&30&45&60&10&15&35&70\\$B.P.(Y) in mmHg&80&85&125&90&100&135&80&70&100&140\end{array}\right|](https://tex.z-dn.net/?f=%5Cleft%7C%5Cbegin%7Barray%7D%7Bc%7Cccccccccccccc%7D%24Patient%26A%26B%26C%26D%26E%26F%26G%26H%26I%26J%5C%5C%24Age%20%28X%29%20in%20Years%2620%2625%2650%2630%2645%2660%2610%2615%2635%2670%5C%5C%24B.P.%28Y%29%20in%20mmHg%2680%2685%26125%2690%26100%26135%2680%2670%26100%26140%5Cend%7Barray%7D%5Cright%7C)
To determine the product moment correlation coefficient for the data, we follow the steps below:
Step 1: Find the following as it was done in the table below.
![\sum{X}~,~ \sum{Y} ~,~ \sum{X \cdot Y} ~,~ \sum{X^2}~,~and \sum{Y^2}](https://tex.z-dn.net/?f=%5Csum%7BX%7D~%2C~%20%5Csum%7BY%7D%20~%2C~%20%5Csum%7BX%20%5Ccdot%20Y%7D%20~%2C~%20%5Csum%7BX%5E2%7D~%2C~and%20%5Csum%7BY%5E2%7D)
Step 2: Take the sum of every column to obtain:
![\sum{X}=360 ~,~ \sum{Y}=1005 ~,~ \sum{X \cdot Y}=40425 ~,\\~ \sum{X^2}=16500 ~,~ \sum{Y^2}=106475](https://tex.z-dn.net/?f=%5Csum%7BX%7D%3D360%20~%2C~%20%5Csum%7BY%7D%3D1005%20~%2C~%20%5Csum%7BX%20%5Ccdot%20Y%7D%3D40425%20~%2C%5C%5C~%20%5Csum%7BX%5E2%7D%3D16500%20%20~%2C~%20%5Csum%7BY%5E2%7D%3D106475)
Step 3: Use the following formula to find the PMCC.
![r=\dfrac{n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}}{\sqrt{\left[n \sum{X^2}-\left(\sum{X}\right)^2\right] \cdot \left[n \sum{Y^2}-\left(\sum{Y}\right)^2\right]}}](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7Bn%5Ccdot%5Csum%7BXY%7D%20-%20%5Csum%7BX%7D%5Ccdot%5Csum%7BY%7D%7D%7B%5Csqrt%7B%5Cleft%5Bn%20%5Csum%7BX%5E2%7D-%5Cleft%28%5Csum%7BX%7D%5Cright%29%5E2%5Cright%5D%20%5Ccdot%20%5Cleft%5Bn%20%5Csum%7BY%5E2%7D-%5Cleft%28%5Csum%7BY%7D%5Cright%29%5E2%5Cright%5D%7D%7D)
![=\dfrac{10\cdot 40425 - 360\cdot1005}{\sqrt{\left[10*16500}-\left(360\right)^2\right] \cdot \left[10*106475-\left(1005\right)^2\right]}}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B10%5Ccdot%2040425%20-%20360%5Ccdot1005%7D%7B%5Csqrt%7B%5Cleft%5B10%2A16500%7D-%5Cleft%28360%5Cright%29%5E2%5Cright%5D%20%5Ccdot%20%5Cleft%5B10%2A106475-%5Cleft%281005%5Cright%29%5E2%5Cright%5D%7D%7D)
![=\dfrac{42450}{\sqrt{1937265000}}\\=0.9645\\r\approx 0.96$ (correct to 2 decimal places)](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B42450%7D%7B%5Csqrt%7B1937265000%7D%7D%5C%5C%3D0.9645%5C%5Cr%5Capprox%200.96%24%20%28correct%20to%202%20decimal%20places%29)
<u>Interpretation</u>
- When r is closer to 1, there is a strong positive relationship between the variables.
- A value of 0 indicates that there is no relationship between the variables.
- Values close to -1 signal a strong negative relationship between the two variables.
Since r=0.96 which is closer to 1, we conclude that there is a strong relationship between the age and the high blood pressure related deaths in the state.
The least would be 0.015.
Answer:
3
Step-by-step explanation:
12*1/4
=12/4
=3
Given expression: − 11.50 (1.32 + 0.48).
We need to simplify it and get the answer in decimals.
Note: In order to simplify above given expression, we need to apply order to operations.
According to order to operations, we need to simplify parenthesis first.
So, we need to add 1.32 + 0.48 first.
1.32 + 0.48 = 1.80.
So, − 11.50 (1.32 + 0.48) would become -11.50(1.80).
Now, we need to multiply -11.50 by 1.80.
-11.50(1.80) = -20.7.
<h3>Therefore, final answer is -20.7.</h3>
Answer44
Step-by-step explanation:
5+5=10