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
<span><span><span><span><span>14y</span>+112</span>+2</span>−<span>134y</span></span>−12</span><span>=<span><span><span><span><span><span><span>14y</span>+112</span>+2</span>+</span>−<span>134y</span></span>+</span>−12</span></span><span>=<span><span><span><span><span>14y</span>+112</span>+2</span>+<span>−<span>134y</span></span></span>+<span>−12</span></span></span><span>=<span><span>(<span><span>14y</span>+<span>−<span>134y</span></span></span>)</span>+<span>(<span><span>112+2</span>+<span>−12</span></span>)</span></span></span><span>=<span><span>−<span>120y</span></span>+102</span></span>
Answer:
<span>=<span><span>−<span>120y</span></span>+<span>102</span></span></span>
Answer: We can
Step-by-step explanation: 20.00
- 1.97
Answer:
Step-by-step explanation:
