Answer:
We use students' t distribution therefore degrees of freedom is v= n-2
Step-by-step explanation:
<u>Confidence Interval Estimate of Population Regression Co efficient β.</u>
To construct the confidence interval for β, the population regression co efficient , we use b, the sample estimate of β. The sampling distribution of b is normally distributed with mean β and a standard deviation σ.y.x / √(x-x`)². That is the variable z = b - β/σ.y.x / √(x-x`)² is a standard normal variable. But σ.y.x is not known so we use S.y.x and also student's t distribution rather than normal distribution.
t= b - β/S.y.x / √(x-x`)² = b - β/Sb [Sb = S.y.x / √(x-x`)²]
with v= n-2 degrees of freedom.
Consequently
P [ - t α/2< b - β/Sb < t α/2] = 1- α
or
P [ b- t α/2 Sb< β < b+ t α/2 Sb] = 1- α
Hence a 100( 1-α) percent confidence for β the population regression coefficient for a particular sample size n <30 is given by
b± t α/2 Sb
Using the same statistic a confidence interval for α can be constructed in the same way for β replacing a with b and Sa with Sb.
a± t α/2 Sa
Using the t statistic we may construct the confidence interval for U.y.x for the given value X0 in the same manner
Y~0 ± t α/2(n-2) SY~
Y~0= a+b X0
Answer: 
Step-by-step explanation:
<h3>
The exercise is: " Evaluate 
when 
and 
</h3>
Given the following expression:
You can follow these steps in order to evaluate it:
1. Substitute and into the expression provided in the exercise:
2. Solve the multiplications. Remember that:
Then:
3. Reduce the fraction. Notice that the numerator 6 and the denomiantor 4 can be both divided by 2. Then:
4. Solve the addition:
Since the number 21 has a denominator 1, the Least Common Denominator is:
Then, the sum is:
Answer:
Step-by-step explanation:
There is nothing to answer so put it out for help
Answer:
4
Step-by-step explanation:
Firstly simplify your brackets...,
; 4(a^2 + 2b) = 4a^2 + 8b...then substitute it onto the bracket
; 4a^2 + 8b - 2b
; 4a^2 + 6b....,then substitute with the given values of a and b
; 4(2)^2)+ 6(-2)
; 16 - 12 = 4
Answer:
a) 
b) When t = 10, Q = 7.845.
Step-by-step explanation:
The value of a quantity after t years is given by the following formula:
In which 
is the initial quantity and r is the rate that it changes. If it increases, r is positive. If it decreases, r is negative.
a) Write a formula for Q as a function of t.
The initial value of a quantity Q (at year t = 0) is 112.8.
This means that 
.
The quantity is decreasing by 23.4% per year.
This means that 
So
b) What is the value of Q when t = 10?
This is Q(10).
When t = 10, Q = 7.845.
