Answered: he peanut crop was harvested from five…

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

The peanut crop was harvested from five fields of various area. The following data are the mass of the crop from each field y (in kilograms) and the field area x (in hectares).

y	7360	15760	13690	20080	12910
x	2.34	3.92	3.35	4.56	2.56

Round your intermediate answers to four decimal places (e.g. 98.7654).

(a) Fit the simple linear regression model using the method of least squares. Find the estimate of σ2.
Round your answer to the nearest integer (e.g. 9876).
σ^2=

(b) What change in the mean mass is expected when the field area changes by 1 hectare?
Round your answer to the nearest integer (e.g. 9876).
β^1=

(c) Calculate the fitted value of y corresponding to x=3.92. Find the corresponding residual.
Round your answer to the nearest integer (e.g. 9876).
y^=

Round your answer to the nearest integer (e.g. 9876).
e=

(d) Estimate the mean mass of the crop harvested from 4.5 hectares.
Round your answer to the nearest integer (e.g. 9876).
y^=

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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