Full Question:
The data show systolic and diastolic blood pressure of certain people. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted diastolic pressure for a person with a systolic reading of 113. use a significance level of 0.05.
Systolic| 150 129 142 112 134 122 126 120
Diastolic| 88 96 106 80 98 63 95 64
a. What is the regression equation?
^y = __ + __x (Round to two decimal places as needed.)
b. What is the best predicted value?
^y is about __ (Round to one decimal place as needed.)
Answer:
A. yhat = a + bx = -10.64 + 0.75x
B. 74.0
Step-by-step explanation:
A. To find the regression equation here, we apply the formulas and then apply it to find the value of y given value of x:
calculate xbar and ybar which is the average of the variables:
Where n(number of values in x or y)=8
xbar = sum of x/n = 129.375
ybar = sum of y/n = 86.25
to calculate b
b= [Sum x^2 * Sum y - Sum x * Sum x*y] / [N*Sum x^2 - (Sum x)^2]
b = 0.74891
To calculate a
a = ybar - b * xbar = -10.64023
Regression equation:
y=mx+b= -10.64 + 0.75x
B. given x = 113,
y = -10.64023 + 0.74891 * 113
y= 74.0
r²h and you know all of your numbers other than h so you plug all that in. 100=3.14×2²×h → 100=3.14×4×h → 100=12.56×h → Divide 12.56 from both sides 100÷12.56=12.56×h÷12.56 → 7.96cm=h.