Typically, blood pressure
(Y)
increases with age
(x)
. The summary statistics of 15 individuals older than age 40 years are given in Table 1 below. [ ]
??151,27
Say
Y=\beta _(0)+\beta _(1)x+\epsi lon
is used to describe the relationship between
Y
and
x
. Answer the following questions and please round the final numerical results to two decimal places. (1). Derive the least square estimates of
\beta _(0)
and
\beta _(1)
. (2). Suppose we know that the sum of squares of residuals is 3889.43 and that
([n,\sum_(i=1)^n x_(i)],[\sum_(i=1)^n x_(i),\sum_(i=1)^n x_(i)^(2)])^(-1)=([3.2570,-0.0586],[-0.0586,0.0011])
(2-1). Please derive a
90%
confidence interval for the mean value of the blood pressure for a 50 -year old person. (2-2). Please conduct a test for the significance of the straight line model at a significance level of
5%
. Answer all questions please.