) How many degrees of freedom are available for hypothesis tests and confidence intervals for single regression coefficient

We use students' t distribution therefore degrees of freedom is v= n-2

Step-by-step explanation:

Confidence Interval Estimate of Population Regression Co efficient β.

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

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct