Question

The Senator of Azenator State, is worried about the rising numbers in high blood pressure related deaths in his Jurisdiction and wants an end to this canker. A reputable medical research officer has claimed that, the situation is probably as a result of the ageing population of his State. The blood pressures, Y (mmHg), and Ages, X (years) of 10 hospital patients were sampled from Azenator State and summarized below.

NB: Approximate to 2 decimal places

Use the table to answer the questions that follow;

i) Calculate the product moment correlation coefficient for the data and interpret your result.

ii) If the Senator decides to purchase and distribute Norvasc (a medicine that reduces blood pressure), based on your results in (i), which age group (youth or old adults) should be given priority? Briefly explain your answer.

iii) Give a reason to support fitting a regression model of the form ? = ? + ?? + ? , where (a) is the y-intercept or constant, (b) is the slope of the function, (y) is the blood pressure of a patient, (X) is the age of a patient and ? is the error term.

iv) From the model specified in (iii), estimate the values of (a) and (b) and interpret the values

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

BP(Y) in (mmHg)

80

85

125

90

100

135

80

70

100

140

v) What is the blood pressure of an infant at birth?

vi) Predict the blood pressure of a patient who is 90 years old.

vii) Estimate the coefficient of determination and interpret your result.

[Total: 20 Marks]

Answer 1

(i)

Correlation coefficient is computed as follows

Interpretation : The value of correlation coefficient r=0.9645 indicates that it is approximately perfect positive correlation i.e. with the increase in age , increases the Blood Pressure.

ii)

The Blood Pressure should be in the range of ( 80/120 ) . Here, from the given data Age Group of 50 years and above should be given priority .

iii)

iv)

Y - intercept = 57.33051

Slope = 1.19915

v)

What is the blood pressure of an infant at birth?

Taking x = 0 , we get = 57.33

vi)

Predict the blood pressure of a patient who is 90 years old.

Taking x=90 , we get = 1.19*(90) + 57.33 = 164.43.

vii)

Estimate the coefficient of determination and interpret your result.

Coefficient of Determination = 1 - ( SSE / SST )

SSE =

SST =

Coefficient of Determination (R2) = 1 - ( 382.10 / 5472.50 )

                                         = 1 - 0.0698

                                         = 0.9302

R2 indicates the 93.02% of the variance in the dependent variable (BP) that is predicted or explained by linear regression and the predictor variable (Age).