1. Consider the normal linear regression model Y~ N(a + Bx, o²). Data pairs (xi, yi) of sample size n= 43 have been collected and summarised below: n n n n n Σ |xi = 11.3, Σw = 154.8, Σy = 19.2, Σy =135, & Σαϊy = 24.9. i=1 i=1 i=1 i=1 i=1 From this data, compute the least-squares estimates for a and ß. Given that the residual variance estimate is s² = 0.0544, evaluate the expected value and 95% prediction interval a future response Yo at x = 10. Clearly state the definitions/formulas you are using in this question and report the pre- dicted value and interval correct to 2 decimal places. From the given information, provide a brief comment about this prediction.

1. Consider the normal linear regression model Y~ N(a + Bx, o²). Data pairs (xi, yi) of sample size n= 43 have been collected and summarised below: n n n n n Σ |xi = 11.3, Σw = 154.8, Σy = 19.2, Σy =135, & Σαϊy = 24.9. i=1 i=1 i=1 i=1 i=1 From this data, compute the least-squares estimates for a and ß. Given that the residual variance estimate is s² = 0.0544, evaluate the expected value and 95% prediction interval a future response Yo at x = 10. Clearly state the definitions/formulas you are using in this question and report the pre- dicted value and interval correct to 2 decimal places. From the given information, provide a brief comment about this prediction.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

1. Consider the normal linear regression model Y~ N(a + Bx, o²). Data pairs (xi, yi) of
43 have been collected and summarised below:
sample size n
n
Σ Xi =
i=1
=
n
n
n
n
11.3, Σx = 154.8, Σy = 19.2, Συ = 135, & Σαϊyi
£x
i=1
i=1
i=1
i=1
24.9.
From this data, compute the least-squares estimates for a and B. Given that the residual
variance estimate is s² = 0.0544, evaluate the expected value and 95% prediction interval
a future response Yo at xo = 10.
Clearly state the definitions/formulas you are using in this question and report the pre-
dicted value and interval correct to 2 decimal places. From the given information, provide
a brief comment about this prediction.

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