A researcher conducts a multiple regression with Y as the dependent variable and X1,X2, X3 and X4 as explanatory variables. Using the regression output below, fullydescribe this model and discuss important parts of the output. What is the predictedvalue of Y if X1 = 3, X2 = 15, X3 = 7 and X4 = 0.003?%3DSUMMARY OUTPUTRegression StaisticsMuliple RR SquareAdjusted R SquareStandard EmorObservations0.72360.52360.51595.3928252ANOVASignificance F1. 10662E-38SSMSRegressionResidual1973 939229.082067.87497895.75677183.25994247Total25115079.0166Upper 95%33.4049CoefficientsStandard Erort StatPvalue2.2273 0.026830873Lower 95%7.95942.0508InterceptX117.72781.55830.27505.66624.05265E-081.01662.0999X21.83760.19979.19991.4442-74708-3721 43241.55861E-172.2310X355100-5.53487.94036E-08-3.5492X4-3.10791887 8435-0.00160.9986877883715 2166

Solution: The regression output is given. From the given output, the coefficient of intercept is…

A researcher conducts a multiple regression with Y as the dependent variable and X1, X2, X3 and X4 as explanatory variables. Using the regression output below, fully describe this model and discuss important parts of the output. What is the predicted value of Y if X1 = 3, X2 = 15, X3 = 7 and X4 = 0.003? %3D %3D SUMMARY OUIPUT Regression Statistics Muliple R R Square Adjusted R Square Standard Emor Observations 0.7236 0.5236 0.5159 5.3928 252 ANOVA df SS MS Significance F 1973 9392 29.0820 67.8749 Regression Residual 7895.7567 7183.2599 15079.0166 1.10662E-38 247 Total 251 Upper 95% 33.4049 2.0999 t Stat Pvalue 2.2273 0.026830873 Coefficients Standard Eror Lower 95% Intercept X1 17.7278 7.9594 2.0508 1.5583 0.2750 5.6662 4.05265E 08 1.0166 X2 1.8376 55100 -3.1079 0.1997 9.1999 1.55861E-17 1.4442 2.2310 X3 0.9955 1887 8435 -5.5348 7.94036E-08 -74708 -3.5492 X4 0.0016 0 998687788 -3721 4324 3715.2166

A researcher conducts a multiple regression with Y as the dependent variable and X1, X2, X3 and X4 as explanatory variables. Using the regression output below, fully describe this model and discuss important parts of the output. What is the predicted value of Y if X1 = 3, X2 = 15, X3 = 7 and X4 = 0.003? %3D %3D SUMMARY OUIPUT Regression Statistics Muliple R R Square Adjusted R Square Standard Emor Observations 0.7236 0.5236 0.5159 5.3928 252 ANOVA df SS MS Significance F 1973 9392 29.0820 67.8749 Regression Residual 7895.7567 7183.2599 15079.0166 1.10662E-38 247 Total 251 Upper 95% 33.4049 2.0999 t Stat Pvalue 2.2273 0.026830873 Coefficients Standard Eror Lower 95% Intercept X1 17.7278 7.9594 2.0508 1.5583 0.2750 5.6662 4.05265E 08 1.0166 X2 1.8376 55100 -3.1079 0.1997 9.1999 1.55861E-17 1.4442 2.2310 X3 0.9955 1887 8435 -5.5348 7.94036E-08 -74708 -3.5492 X4 0.0016 0 998687788 -3721 4324 3715.2166

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

A researcher conducts a multiple regression with Y as the dependent variable and X1,
X2, X3 and X4 as explanatory variables. Using the regression output below, fully
describe this model and discuss important parts of the output. What is the predicted
value of Y if X1 = 3, X2 = 15, X3 = 7 and X4 = 0.003?
%3D
SUMMARY OUTPUT
Regression Staistics
Muliple R
R Square
Adjusted R Square
Standard Emor
Observations
0.7236
0.5236
0.5159
5.3928
252
ANOVA
Significance F
1. 10662E-38
SS
MS
Regression
Residual
1973 9392
29.0820
67.8749
7895.7567
7183.2599
4
247
Total
251
15079.0166
Upper 95%
33.4049
Coefficients
Standard Eror
t Stat
Pvalue
2.2273 0.026830873
Lower 95%
7.9594
2.0508
Intercept
X1
17.7278
1.5583
0.2750
5.6662
4.05265E-08
1.0166
2.0999
X2
1.8376
0.1997
9.1999
1.4442
-74708
-3721 4324
1.55861E-17
2.2310
X3
55100
-5.5348
7.94036E-08
-3.5492
X4
-3.1079
1887 8435
-0.0016
0.998687788
3715 2166

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