Math, asked by Nolansia4099, 12 hours ago

the following results were obtained from records of age (x) and symbolic blood pressure (y) of a group of 10 men: mean x=53 mean y=142 and variance x= 130 and variance y=165 find the appropriate regression equation and use it to estimate the blood pressure of a man whose age is 45.​

Answers

Answered by srivastavaanusha63
0

Answer:

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Answered by Dhruv4886
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Given:

the following results were obtained from records of age (x) and symbolic blood pressure (y) of a group of 10 men Mean X=53 Y=142 and variance X=130 Y=142 and \sum(x_{i}-\bar{x})(y_{i}-\bar{y})=910

To Find:

find the appropriate regression equation and use it to estimate the blood pressure of a man whose age is 45

Solution:

It is given that X is for age and Y is for symbolic blood pressure

now using the formula for variance

Var(x)=\frac{\sum(x_{i}-\bar{x})^2}{n}\\130=\frac{\sum(x_{i}-\bar{x})^2}{10}\\\\\sum(x_{i}-\bar{x})^2=1300

now calculating the value ofb_{yx}

b_{yx}=\frac{\sum(x_{i}-\bar{x})(y_{i}-\bar{y})}{\sum(x_{i}-\bar{x})^2} \\=\frac{910}{1300}\\=0.7\\

Now the regression equation of symbolic blood pressure(Y) on their age(X) is

(Y-\bar{y})=b_{yx}(X-\bar{x}\\(Y-142)=0.7(X-53)\\Y=0.7X-53+142\\Y=0.7X+89

Now for X=45

Y=0.7*45+89\\=120.5

Hence, the man of age 45 has a symbolic blood pressure of 120.5

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