Question

The data show systolic and diastolic blood pressure of certain people. Find the regression​ equation, letting the systolic reading be the independent​ (x) variable. If one of these people has a systolic blood pressure of 113mm​ Hg, what is the best predicted diastolic blood​ pressure?

systolic: 150 129 142 112 134 122 126 120

diastolic: 88 96 106 80 98 63 95 64

y = _ + _X

Answer 1

Given that, the data of systolic and diastolic blood pressure of certain people.

We want to find regression​ equation, letting the systolic reading be the independent​ (X) variable and diastolic reading be the dependent​ (Y).

A linear regression equation is given by in the form, Y = a +bX

[ Where a, b are constant and estimated by least square method,

, and

Table for calculation:-

Xi = Systolic	Yi = Diastolic
150	88	20.625	1.75	36.09375	425.3906
129	96	-0.375	9.75	-3.65625	0.140625
142	106	12.625	19.75	249.3438	159.3906
112	80	-17.375	-6.25	108.5938	301.8906
134	98	4.625	11.75	54.34375	21.39063
122	63	-7.375	-23.25	171.4688	54.39063
126	95	-3.375	8.75	-29.5313	11.39063
120	64	-9.375	-22.25	208.5938	87.89063
Total=1035	Total=690			Total=795.25	Total=1061.875

Calculation: All the values are putting from table.

• Sample mean of X

• Sample mean of Y

• Sample mean of Var(X)

• Covariance between X and Y

• Estimate of b

• Estimate of a

Answer:-   So the regression equation is given by,

Now, If one of these people has a systolic blood pressure of 113 mm​ Hg, then the diastolic blood​ pressure of that people is given by the regression equation,

Answer:- If one of these people has a systolic blood pressure of 113 mm​ Hg, then the diastolic blood​ pressure of that people is 73.9869 mm Hg