Answered: SUMMARY OUTPUT Regression Statistics…

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

In this question, we want to analyse the total energy production in Australia on a monthly basis from 2010 to 2022. The energy production is measured in gigawatt-hours (GWh). This covers a range of energy sources including coal, electricity supplied, fossil fuels, natural gas, renewables, solar and others.

a) To analyse the energy production, we start by defining the following variables:

total_prod = is the total monthly energy production from different sources (GWh)

Mean = constant values of 1’s for all the production

Exhibit 10 below shows the regression output from a regression of total_prod (dependent variable) on Mean (independent variable):

i) What does the coefficient of the “mean” value tell us?

ii) State and in the context, interpret the 90% confidence interval for the “Australia energy production”.

iii) Explain the concept of “repeated sampling” and give a “mathematical” interpretation of the 90% confidence interval using the given confidence interval from Exhibit 10.

iv) It appears that the confidence interval in the Exhibit 10 is fairly narrow.

Discuss what would be the main factor for this.

Give evidence in your explanation.

SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R
Square
Standard Error
Observations
ANOVA
Regression
Residual
Total
Intercept
mean
0.62629
0.39224
0.39195
7883.1697
3446
df
1
3445
3446
0
Coefficients Standard Error t Stat
#N/A
#N/A
47.153
6332.1614
Exhibit 10
SS
MS
F
1.382E+11 1E+11 2223.3993
2.141E+11 6E+07
3.523E+11
134.2899
P-value
#N/A
0
Significance F
0
Lower 90.0% Upper 90.0%
#N/A
#N/A
6553.108
6111.215

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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