Question

QUESTION 1

Answer 1

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:

$\left|\begin{array}{c|ccccccccccccc} Patient&A&B&C&D&E&F&G&H&I&J\\ Age (X) in Years&20&25&50&30&45&60&10&15&35&70\\ B.P.(Y) in mmHg&80&85&125&90&100&135&80&70&100&140\end{array}\right|$

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.

$\sum{X}~,~ \sum{Y} ~,~ \sum{X \cdot Y} ~,~ \sum{X^2}~,~and \sum{Y^2}$

Step 2: Take the sum of every column to obtain:

$\sum{X}=360 ~,~ \sum{Y}=1005 ~,~ \sum{X \cdot Y}=40425 ~,\\~ \sum{X^2}=16500 ~,~ \sum{Y^2}=106475$

Step 3: Use the following formula to find the PMCC.

$r=\dfrac{n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}}{\sqrt{\left[n \sum{X^2}-\left(\sum{X}\right)^2\right] \cdot \left[n \sum{Y^2}-\left(\sum{Y}\right)^2\right]}}$

$=\dfrac{10\cdot 40425 - 360\cdot1005}{\sqrt{\left[10*16500}-\left(360\right)^2\right] \cdot \left[10*106475-\left(1005\right)^2\right]}}$

$=\dfrac{42450}{\sqrt{1937265000}}\\=0.9645\\r\approx 0.96 (correct to 2 decimal places)$

Interpretation

• 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.