Question

QUESTION 1 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. 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 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 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.

Answer 1

Let us organize the data to  get the sum and the sum of squares to calculate some needed Values.

	X	Y	X^2	Y^2	x*y
	20	80	400	6400	1600
	25	85	625	7225	2125
	50	125	2500	15625	6250
	30	90	900	8100	2700
	45	100	2025	10000	4500
	60	135	3600	18225	8100
	10	80	100	6400	800
	15	70	225	4900	1050
	35	100	1225	10000	3500
	70	140	4900	19600	9800
Total	360	1005	16500	106475	40425

Our n=10.

i) Calculate the product moment correlation coefficient for the data and interpret your result. (3 Marks)

The product moment correlation is given by

  

  

The product moment correlation coefficient for the data=0.9645. The correlation coefficient is quite high and positive. This indicates that there is a strong liner relationship between age and Blood pressure.As age increases, the blood pressure also increases.

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.

It is established that the age and the BP are linearly related and it also indicates that the BP raises as people become old. Hence the Senator should give priority to older people to distribute Norvasc

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. (3 Marks)

As a strong degree of linear relationship is established, we might wish to predict BP values for certain age group in order to facilitate relief measure. If we could establish a liner relationship of the form it will certaicertainly aidhe senator.

iv) From the model specified in (iii), estimate the values of (a) and (b) and interpret the values (4 Marks)

The estimate of

  

The estimated equation is .

The value of a is called teh intercept which is the blood pressure when the age is 0 or at birth which is 57.3305 mmHg. The value of b is called the slope which is 1.1992. This indicates whenever a person gets an year older, the BP raises by 1.1992 mmHg.

v) What is the blood pressure of an infant at birth? (2 Marks)

The BP of an infant at birth is 57.3305 mmHg.

vi).  Predict the blood pressure of a patient who is 90 years old. (2 Marks)

When a person is 90 years old then the blood pressure is teh value of y when x=90.

  ~165 mmHg.

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

The coefficient of determination is given by . Here it is

  

This indicates that the estimated linear model could explain 93.03% of the total variation of the data.