The blood pressures, p mmHg, and the ages, t years, of 7 hospital patients are shown in the table below - Edexcel - A-Level Maths Statistics - Question 6 - 2010 - Paper 1

The product moment correlation coefficient, denoted as $r$, is calculated using the formula:

$r = \frac{nS_{pt} - S_{t}S_{p}}{\sqrt{(nS_{t^2} - S_{t}^2)(nS_{p^2} - S_{p}^2)}}$

Substituting the values, we find:

• $n=7$, $S_{pt} = 106397$, $S_{t} = 833$, $S_{p} = 7270$

After calculations, $r \approx 0.7013$.

The correlation coefficient $r \approx 0.7013$ indicates a strong positive correlation between age and blood pressure. This suggests that as age increases, blood pressure tends to increase.

To create the scatter diagram, plot age on the x-axis and blood pressure on the y-axis using the following points:

• (42, 98)
• (74, 130)
• (48, 120)
• (35, 181)
• (56, 135)
• (26, 120)
• (60, 135)

Ensure to label the axes appropriately.

The regression line can be expressed as:

$p = a + bt$

Where:

• $b = \frac{nS_{pt} - S_{t}S_{p}}{nS_{t^2} - S_{t}^2}$
• After calculating, $b \approx 1.50946$ and the intercept $a = S_{p}/n - b(S_{t}/n)$, giving $a \approx -15.84$.

Thus, the regression line equation is: $p = 1.50946t - 15.84$

To plot the regression line on the scatter diagram, use the calculated equation: $p = 1.50946t - 15.84$

Choose several values of $t$ (ages) to compute corresponding values of $p$ (blood pressures) and draw the line on the scatter plot.

To estimate the blood pressure for a 40-year-old patient, substitute $t = 40$ into the regression line equation: $p = 1.50946(40) - 15.84 \approx 63.78$

Therefore, the estimated blood pressure is approximately 63.78 mmHg.