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hests of tree-pipits, the following results were obtained for 1 2 3 4 5 6 7 8 n) 16.3 16.6 17.0 16.9 16.3 16.7 16.5 16.2 22.7 23.3 24.0 23.6 22.1 21.8 21.1 23.4 1 10 10 ri=2739.71, L si =5256.89, ) ®i!=3792.2 i=1 i=1 sample correlation coefficient between the breadth and squares regression line for predicting the egg length giver Use your fitted regression line to predict the egg length ch 16.4 mm. nce level 5%, test the hypothesis that the slope of your you may assume that for a fitted least squares regression lin Ope 3 has variance Var(3) = ô² Σ=1(x − x)2’

hests of tree-pipits, the following results were obtained for 1 2 3 4 5 6 7 8 n) 16.3 16.6 17.0 16.9 16.3 16.7 16.5 16.2 22.7 23.3 24.0 23.6 22.1 21.8 21.1 23.4 1 10 10 ri=2739.71, L si =5256.89, ) ®i!=3792.2 i=1 i=1 sample correlation coefficient between the breadth and squares regression line for predicting the egg length giver Use your fitted regression line to predict the egg length ch 16.4 mm. nce level 5%, test the hypothesis that the slope of your you may assume that for a fitted least squares regression lin Ope 3 has variance Var(3) = ô² Σ=1(x − x)2’

MATLAB: An Introduction with Applications
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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could you please do parts a,b and c

B3. In a 1901 study by Oswald Latter of the length and breadth of cuckoo (Cuculus Canorus) eggs laid in the nests of tree-pipits, the following results were obtained for ten randomly selected eggs. egg 1 2 3 4 breadth x (mm) | 16.3 16.6 17.0 16.9 16.3 length y, (mm) 22.7 23.3 24.0 23.6 22.1 10 10 10 Σx = 2739.71, Σy = 5256.89, Σwiyi = i=1 i=1 i=1 (a) Obtain the sample correlation coefficient between the breadth and the length of the eggs. 5 6 7 8 9 10 16.7 16.5 16.2 16.3 16.7 21.8 21.1 23.4 23.8 23.3 (b) Fit a least squares regression line for predicting the egg length given the breadth of an egg. Use your fitted regression line to predict the egg length for a new egg with breadth 16.4 mm. (c) At significance level 5%, test the hypothesis that the slope of your regression line equals zero. Hint: in part (c) you may assume that for a fitted least squares regression line y = = â+3x, the estimated slope has variance ô² ô² 1 (x₂ − x) ²¹ where the estimated variance of the data about the fitted line satisfies = 3792.2 Var(B) = 1 n-2 In n n Σ(Yi − y)² – ß² Σ(xi − x)² *²0-2²) i=1 i=1
Transcribed Image Text:B3. In a 1901 study by Oswald Latter of the length and breadth of cuckoo (Cuculus Canorus) eggs laid in the nests of tree-pipits, the following results were obtained for ten randomly selected eggs. egg 1 2 3 4 breadth x (mm) | 16.3 16.6 17.0 16.9 16.3 length y, (mm) 22.7 23.3 24.0 23.6 22.1 10 10 10 Σx = 2739.71, Σy = 5256.89, Σwiyi = i=1 i=1 i=1 (a) Obtain the sample correlation coefficient between the breadth and the length of the eggs. 5 6 7 8 9 10 16.7 16.5 16.2 16.3 16.7 21.8 21.1 23.4 23.8 23.3 (b) Fit a least squares regression line for predicting the egg length given the breadth of an egg. Use your fitted regression line to predict the egg length for a new egg with breadth 16.4 mm. (c) At significance level 5%, test the hypothesis that the slope of your regression line equals zero. Hint: in part (c) you may assume that for a fitted least squares regression line y = = â+3x, the estimated slope has variance ô² ô² 1 (x₂ − x) ²¹ where the estimated variance of the data about the fitted line satisfies = 3792.2 Var(B) = 1 n-2 In n n Σ(Yi − y)² – ß² Σ(xi − x)² *²0-2²) i=1 i=1
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