Answered: Model A: Y= β_0+β_1 X+ε Use the…

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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Model A: Y= β_0+β_1 X+ε
Use the Excel Output from Model A to answer the following questions.
Is X a significant predictor of Y? Interpret the coefficient of X.
sFind the Total Sum of Square. Find Mean Squared Regression (MSR) and Mean Squared Error (MSE)
What is the F-statistic? Is the F statistic significant? (assume critical value is 3.5)
Calculate Y hat. Generate a new column of predictions based on the output from Model A (FYI: You are using your model to forecast outcomes for a set of points that were not used to build your model).
Find the R square. Is this a good model? Explain why or why not.

Part I: Regression Basics
SUMMARY OUTPUT A
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
ANOVA
Regression
Residual
Total
Obs.
1
2
Regression Statistics
Intercept
X
3
4
X5560 00
8
0.97688814
df
0.939080583
3.277208147
5
1
3
4
Data
Y
23
16
25
28
SS
672.9797
32.22028
Y hat
Standard
Error
Coefficients
t Stat P-value
2.531468531 3.604616 0.702285 0.533087
3.43006993 0.433317 7.915839 0.004203

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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