Given are five observations for two variables, x and y. (Round your answers to two decimal places.) X₁ 1 2 3 4 5 Y₁ (a) Use S = S 4 1 n to 7 (c) Use Spred = SV + 6 10 13 (b) Use ŷ* ±ta/25%* to develop a 95% confidence interval for the expected value of y when x = 5. to (x*- x)² Σ(x; − x)2 to estimate the standard deviation of y* when x = 5. 1 (x*- x)² = S₁1+ + n Σ(x, − x)2 to estimate the standard deviation of an individual value of y when x = 5. (d) Use * ±ta/25 pred to develop a 95% prediction interval for y when x = 5.
Given are five observations for two variables, x and y. (Round your answers to two decimal places.) X₁ 1 2 3 4 5 Y₁ (a) Use S = S 4 1 n to 7 (c) Use Spred = SV + 6 10 13 (b) Use ŷ* ±ta/25%* to develop a 95% confidence interval for the expected value of y when x = 5. to (x*- x)² Σ(x; − x)2 to estimate the standard deviation of y* when x = 5. 1 (x*- x)² = S₁1+ + n Σ(x, − x)2 to estimate the standard deviation of an individual value of y when x = 5. (d) Use * ±ta/25 pred to develop a 95% prediction interval for y when x = 5.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Given are five observations for two variables, x and y. (Round your answers to two decimal places.)
|
xi
|
1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
|
yi
|
4 | 7 | 6 | 10 | 13 |
(a)
Use
sŷ* = s
to estimate the standard deviation of
|
ŷ*
when
x = 5.
(b)
Use
expected value of y when
ŷ* ± t?/2sŷ*
to develop a 95% confidence interval for the x = 5.
to
(c)
Use
to estimate the standard deviation of an individual value of y when
spred = s
1 +
|
x = 5.
(d)
Use
ŷ* ± t?/2spred
to develop a 95% prediction interval for y when
x = 5.
to
Transcribed Image Text:Given are five observations for two variables, x and y. (Round your answers to two decimal places.)
(a) Use s
X;
Yi
Sŷ*
(c) Use s
= S
1 2 3 4
Spred
4
01
= S
7 6
5
10 13
1 (x*- x)²
+
n
Σ(x; − x)2
(b) Use ŷ* ± tu/25ŷ* to develop a 95% confidence interval for the expected value of y when x = 5.
to
to estimate the standard deviation of ŷ* when x = 5.
1 (x* - x)²
1 + +
to estimate the standard deviation of an individual value of y when x = 5.
n
Σ(Χ;
x)²
(d) Use ŷ* ± ta/25 pred to develop a 95% prediction interval for y when x = 5.
to
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Step 1: Determine the given variables.
VIEWStep 2: Find the regression equation and predicted value for x = 5
VIEWStep 3: Find the value of s, sum of ( x - xbar)^2.
VIEWStep 4: Find the estimate of standard deviation of yhat*
VIEWStep 5: Construct 95% confidence interval for expected value of y.
VIEWStep 6: Find the standard deviation for an individual value of y.
VIEWStep 7: Construct prediction interval for y.
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