Question

Find the best predicted value 1.Given n = 15, y(hat)= 12.8 + 4.5x, y(bar)= 23, r = .875, α = 0.05, predict y when x = 2.

Answer 1

a.
Given that,
value of r =0.875
number (n)=15
null, Ho: row(ρ) =0
alternate, H1: row(ρ)!=0
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.16
since our test is two-tailed
reject Ho, if to < -2.16 OR if to > 2.16
we use test statistic (t) = r / sqrt(1-r^2/(n-2))
to=0.875/(sqrt( ( 1-0.875^2 )/(15-2) )
to =6.517
|to | =6.517
critical value
the value of |t α| at los 0.05% is 2.16
we got |to| =6.517 & | t α | =2.16
make decision
hence value of | to | > | t α| and here we reject Ho
ANSWERS
---------------
null, Ho: row(ρ) =0
alternate, H1: row(ρ)!=0
test statistic: 6.517
critical value: -2.16 , 2.16
decision: reject Ho
we have enough evidence to support the claim

b.
y(hat)= 12.8 + 4.5x
predict y when x = 2
y(hat)= 12.8 + (4.5*2)
Y(hat) = 21.8
given value of y(bar)= 23,
predicted value is Y(hat) =21.8