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
What are you trying to say?
Answer:
3m²
Step-by-step explanation:
A square is quadrilateral (four sides) in which all sides are equal. Also, opposite sides are parallel to one another and all the four angles in a square are 90 degrees each.
The area of a square is given as:
Area = length * length
Given that the square has side lengths of m centimeters, therefore:
The area of each square = m cm × m cm = m² cm²
There are three rows of m squares, hence the total number of square is:
Total square = 3 rows * m squares per row = 3m squares
The total area of the square = area of each square * total number of square = m² * 3m = 3m² cm²
(m+6) + (4m+2)
Add 4m to m while adding 2 to 6
Final Answer: 5m+8
