What is the coefficient of determination, and adjusted coefficient of determination? What do these values illustrate? What is the mean squared error for this model? What does it mean? SUMMARYOUTPUTRegression StatisticsMultiple RR SquareAdjusted RSquareStandard Error 0.648011208ObservationsANOVARegressionResidualTotalInterceptfixed acidity;volatile aciditycitric acidresidual sugarchloridesfree sulfurdioxidetotal sulfurdioxidedensitypHsulphatesalcohol0.6004595770.3605517030.356119484df15991587159811 375.754403 34.159491160.419918526CoefficientsSS-0.182563950.01633127-1.874225160.004361333MS666.41071042.1651t StatF81.3479022P-valueStandard63.53751785 -19.6071009463.53751785Error21.96520845 21.194575 1.036359939 0.300192136 -19.607100940.024990553 0.0259485 0.963082682 0.335652752 -0.025906394 0.075887499 -0.025906394 0.075887499-1.08359026 0.12110128 -8.947801896 9.87236E-19 -1.321125565 -0.846054953 -1.321125565 -0.846054953Significance F1.7914E-1450.41928321 -4.470069717 8.37395E-060.00217129 2.008635263 0.044744951Lower 95%Upper 95%Lower 95.0%Upper 95.0%0.14717619 -1.240444878 0.214994246 -0.471244142 0.106116245 -0.471244142 0.1061162450.0150021 1.088599183 0.276495961 -0.013094741 0.04575728 -0.013094741 0.04575728-17.8811638 21.6330999 -0.826565029 0.408607897 -60.31362221-0.41365314 0.19159736 -2.158970991 0.031001886 -0.7894636880.916334413 0.11433747 8.014297061 2.12723E-15 0.6920660570.276197699 0.02648359 10.42901431 1.12303E-24 0.224251206-2.69663236 -1.051817956 -2.69663236 -1.0518179560.000102431 0.008620235 0.000102431 0.008620235-0.00326458 0.00072873 -4.47982984 8.00461E-06 -0.004693951 -0.001835208 -0.004693951 -0.00183520824.55129454 -60.31362221 24.55129454-0.0378426 -0.789463688 -0.03784261.140602768 0.692066057 1.1406027680.328144192 0.224251206 0.328144192

Here Coefficient of Determination is 0.360551703=36.0551703% , explains that the 36.0551703% data…

Answered: What is the coefficient of…

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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What is the coefficient of determination, and adjusted coefficient of determination? What do these values illustrate?

What is the mean squared error for this model? What does it mean?

SUMMARY
OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R
Square
Standard Error 0.648011208
Observations
ANOVA
Regression
Residual
Total
Intercept
fixed acidity;
volatile acidity
citric acid
residual sugar
chlorides
free sulfur
dioxide
total sulfur
dioxide
density
pH
sulphates
alcohol
0.600459577
0.360551703
0.356119484
df
1599
1587
1598
11 375.754403 34.15949116
0.419918526
Coefficients
SS
-0.18256395
0.01633127
-1.87422516
0.004361333
MS
666.4107
1042.1651
t Stat
F
81.3479022
P-value
Standard
63.53751785 -19.60710094
63.53751785
Error
21.96520845 21.194575 1.036359939 0.300192136 -19.60710094
0.024990553 0.0259485 0.963082682 0.335652752 -0.025906394 0.075887499 -0.025906394 0.075887499
-1.08359026 0.12110128 -8.947801896 9.87236E-19 -1.321125565 -0.846054953 -1.321125565 -0.846054953
Significance F
1.7914E-145
0.41928321 -4.470069717 8.37395E-06
0.00217129 2.008635263 0.044744951
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
0.14717619 -1.240444878 0.214994246 -0.471244142 0.106116245 -0.471244142 0.106116245
0.0150021 1.088599183 0.276495961 -0.013094741 0.04575728 -0.013094741 0.04575728
-17.8811638 21.6330999 -0.826565029 0.408607897 -60.31362221
-0.41365314 0.19159736 -2.158970991 0.031001886 -0.789463688
0.916334413 0.11433747 8.014297061 2.12723E-15 0.692066057
0.276197699 0.02648359 10.42901431 1.12303E-24 0.224251206
-2.69663236 -1.051817956 -2.69663236 -1.051817956
0.000102431 0.008620235 0.000102431 0.008620235
-0.00326458 0.00072873 -4.47982984 8.00461E-06 -0.004693951 -0.001835208 -0.004693951 -0.001835208
24.55129454 -60.31362221 24.55129454
-0.0378426 -0.789463688 -0.0378426
1.140602768 0.692066057 1.140602768
0.328144192 0.224251206 0.328144192

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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