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 ( r ) can be calculated using the formula: $r = \frac{n\cdot S_{t,p} - S_t \cdot S_p}{\sqrt{(n \cdot S_t^2 - S_t^2) \cdot (n \cdot S_p^2 - S_p^2)}}$ For these data, we have:

• $n = 7$ (the number of patients)
• substituting the known values: $r = \frac{7 \cdot 18181 - 341 \cdot 1019}{\sqrt{(7 \cdot 116281 - 341^2)(7 \cdot 1038636 - 1019^2)}}$ Calculating this yields:
• $r \approx 0.7013$

The correlation coefficient of approximately 0.7013 indicates a strong positive correlation between age and blood pressure. This suggests that as the age of the patients increases, their blood pressure tends to increase as well.

The scatter diagram should plot age (( t )) on the x-axis and blood pressure (( p )) on the y-axis. Each point on the graph represents a patient, with coordinates given by their age and corresponding blood pressure.

The equation of the regression line can be found using the formula: $p = a + b t$ where:

• ( b = \frac{n \cdot S_{t,p} - S_t \cdot S_p}{n \cdot S_t^2 - S_t^2} )
• ( a = \frac{S_p - b S_t}{n} ) Calculating gives:
• ( b ) as previously determined, and substituting into ( a ) to finally find the regression equation.

Using the equation found in part (e), plot the regression line on the scatter diagram from part (d). The line should visually represent the predicted blood pressure across ages, demonstrating the trend established by the regression analysis.

To estimate the blood pressure, substitute ( t = 40 ) into the regression equation found in part (e). For instance:

• If the regression equation derived is: $p = 45.5 + 1.5(40)$ Then:
• Calculate ( p ) for ( t = 40 ): $p = 45.5 + 60 = 105.5\ mmHg$ This estimate indicates that a 40-year-old patient is expected to have a blood pressure of approximately 105.5 mmHg.