1. What is the coefficient of determination and adjusted coefficient of determination? What do these values illustrate?2. At what point/value is each independent variable significant? What does a 1 unit increase in each independent variable do to the dependent variable?3. What is the mean squared error for this model? What does it mean? ASUMMARY1 OUTPUTWN234 Multiple R5 R SquareRegression Statistics7Adjusted R6 SquareStandard ErrorObservations8910 ANOVA1112 Regression13 Residual14 Total151617 Intercept18 fixed acidity;volatile acidity1920 citric acidresidual sugar2122 chloridesfree sulfur23 dioxidetotal sulfurB24 dioxide25 density26 pH27 sulphates28 alcohol000.6004595770.3605517030.3561194840.648011208df1599сCoefficientsSSD11 375.7544028 34.159491161587 666.4107004 0.4199185261598 1042.165103StandardError21.96520845 21.1945750.024990553 0.025948502-1.083590259 0.12110128MSt StatEFP-valueF81.3479022 1.7914E-145Significance F-1.874225158 0.419283205 -4.470069717 8.37395E-060.004361333 0.002171292 2.008635263 0.044744951Lower 95%GUpper 95%HLower 95.0%|Upper 95.0%1.036359939 0.300192136 -19.60710094 63.53751785 -19.60710094 63.537517850.963082682 0.335652752 -0.025906394 0.075887499 -0.025906394 0.075887499-8.947801896 9.87236E-19 -1.321125565 -0.846054953 -1.321125565 -0.846054953-0.182563948 0.147176188 -1.240444878 0.214994246 -0.471244142 0.106116245 -0.471244142 0.1061162450.01633127 0.015002096 1.088599183 0.276495961 -0.013094741 0.04575728 -0.013094741 0.04575728-2.69663236 -1.051817956 -2.69663236 -1.0518179560.000102431 0.008620235 0.000102431 0.008620235-0.00326458 0.000728729 -4.47982984 8.00461E-06 -0.004693951 -0.001835208 -0.004693951 -0.001835208-17.88116384 21.63309988 -0.826565029 0.408607897 -60.31362221 24.55129454 -60.31362221 24.55129454-0.413653144 0.191597361 -2.158970991 0.031001886 -0.789463688 -0.0378426 -0.7894636880.916334413 0.114337465 8.014297061 2.12723E-15 0.692066057 1.140602768 0.6920660570.276197699 0.026483586 10.42901431 1.12303E-24 0.224251206 0.328144192 0.224251206-0.03784261.1406027680.328144192

Given: We are provided with summary output as shown in the table.1. The coefficient of determination is given by; R-square=R2=0.360551703≅0.3606≅36.06% R-square illustrates the percentage of variation in the dependent variable that is explained by the independent variable. Here 36.06% of variation in explained by the explanatory variables. The adjusted coefficient of determination is given by; Adjusted R2=0.356119484≅0.3561≅35.61% Adjusted R-square is used to compare the goodness-of-fit for the regression model that contains large numbers of explanatory variables. A higher Adjusted R-square means that the model fits the data well.2. Each independent variable is significant at the p-value. We check the significance of the variable by using the p-value. If the p-value is less than the significance level then we consider the result as statistically significant. A one unit increase in each independent variable, increases the dependent variable by the value of corresponding regression coefficient if it is positive and decreases the dependent variable by the value of corresponding regression coefficient if it is negative. 3. The mean squared error for the model is given by Mean Square Residual. MSR=0.419918526 ≅0.4199 The Mean square residual is defined as the mean or average of the square of the differences between actual and the estimated values.

Answered: 1. 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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Question

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

2. At what point/value is each independent variable significant? What does a 1 unit increase in each independent variable do to the dependent variable?

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

A
SUMMARY
1 OUTPUT
WN
2
3
4 Multiple R
5 R Square
Regression Statistics
7
Adjusted R
6 Square
Standard Error
Observations
8
9
10 ANOVA
11
12 Regression
13 Residual
14 Total
15
16
17 Intercept
18 fixed acidity;
volatile acidity
19
20 citric acid
residual sugar
21
22 chlorides
free sulfur
23 dioxide
total sulfur
B
24 dioxide
25 density
26 pH
27 sulphates
28 alcohol
00
0.600459577
0.360551703
0.356119484
0.648011208
df
1599
с
Coefficients
SS
D
11 375.7544028 34.15949116
1587 666.4107004 0.419918526
1598 1042.165103
Standard
Error
21.96520845 21.194575
0.024990553 0.025948502
-1.083590259 0.12110128
MS
t Stat
E
F
P-value
F
81.3479022 1.7914E-145
Significance F
-1.874225158 0.419283205 -4.470069717 8.37395E-06
0.004361333 0.002171292 2.008635263 0.044744951
Lower 95%
G
Upper 95%
H
Lower 95.0%
|
Upper 95.0%
1.036359939 0.300192136 -19.60710094 63.53751785 -19.60710094 63.53751785
0.963082682 0.335652752 -0.025906394 0.075887499 -0.025906394 0.075887499
-8.947801896 9.87236E-19 -1.321125565 -0.846054953 -1.321125565 -0.846054953
-0.182563948 0.147176188 -1.240444878 0.214994246 -0.471244142 0.106116245 -0.471244142 0.106116245
0.01633127 0.015002096 1.088599183 0.276495961 -0.013094741 0.04575728 -0.013094741 0.04575728
-2.69663236 -1.051817956 -2.69663236 -1.051817956
0.000102431 0.008620235 0.000102431 0.008620235
-0.00326458 0.000728729 -4.47982984 8.00461E-06 -0.004693951 -0.001835208 -0.004693951 -0.001835208
-17.88116384 21.63309988 -0.826565029 0.408607897 -60.31362221 24.55129454 -60.31362221 24.55129454
-0.413653144 0.191597361 -2.158970991 0.031001886 -0.789463688 -0.0378426 -0.789463688
0.916334413 0.114337465 8.014297061 2.12723E-15 0.692066057 1.140602768 0.692066057
0.276197699 0.026483586 10.42901431 1.12303E-24 0.224251206 0.328144192 0.224251206
-0.0378426
1.140602768
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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