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Introduction
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When you have one dependent variable and several independent variables and want to determine which one of them has more impact or contribution to the dependent variable, a Multiple Regression is what you need.
Greetings from the world of multiple regression, a potent statistical method for analyzing the complex relationships between a number of variables. In the field of data science and statistical analysis, multiple regression is crucial in identifying the underlying causes of a given outcome. Whether you're an experienced data scientist or a curious enthusiast, this article will provide you the knowledge and skills you need to unlock the potential of multiple regression and glean insightful information from your data.
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An Example
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Below is the example of the Multiple regression application In Matlab from one dependent variable and 5 independent variables. We print the result so we can interpreting it easily. Here is the code:
% Generate random data for demonstration
rng('default') % For reproducibility
n = 100; % Number of data points
dependent_var = randn(n, 1); % Dependent variable (response)
independent_vars = randn(n, 5); % Independent variables (predictors)
% Perform multiple regression
X = [ones(n, 1), independent_vars]; % Add intercept term
[beta,~,~,~,stats] = regress(dependent_var, X); % Multiple regression
% Display the results
disp('Multiple Regression Results:');
disp('----------------------------');
disp(['R-square: ', num2str(stats(1))]);
disp(['Adjusted R-square: ', num2str(stats(2))]);
disp(['F-statistic: ', num2str(stats(3))]);
disp(['p-value (F-statistic): ', num2str(stats(4))]);
disp('----------------------------');
disp('Coefficients:');
disp('----------------------------');
disp(['Intercept: ', num2str(beta(1))]);
disp(['Independent Variable 1: ', num2str(beta(2))]);
disp(['Independent Variable 2: ', num2str(beta(3))]);
disp(['Independent Variable 3: ', num2str(beta(4))]);
disp(['Independent Variable 4: ', num2str(beta(5))]);
disp(['Independent Variable 5: ', num2str(beta(6))]);
disp('----------------------------');
By running this code, you'll get this:
Multiple Regression Results:
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R-square: 0.081007
Adjusted R-square: 1.6572
F-statistic: 0.15264
p-value (F-statistic): 1.3078
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Coefficients:
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Intercept: 0.16381
Independent Variable 1: 0.12976
Independent Variable 2: 0.18573
Independent Variable 3: 0.16405
Independent Variable 4: 0.27308
Independent Variable 5: -0.099852
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Interpretation:
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According to the result above, we can interpret this result as follow:
R-square (R2): The R-square number indicates how much of the variance in the dependent variable can be accounted for by the independent variables. In this case, the R-square is approximately 0.081, which means that about 8.1% of the variance in the dependent variable is explained by the independent variables.
Adjusted R-square: The adjusted R-square changes the R-square value based on the number of independent variables and sample size. The R-square is penalized for containing extra variables that might not be important. In this instance, the corrected R-square is 1.6572, which indicates that the model does not well fit the data and that the independent variables have little explanatory power.
The overall significance of the regression model is tested using the F-statistic. It contrasts the variation that the model explains with the variation that is not explained. The F-statistic in this instance is 0.15264, and the corresponding p-value is 1.3078. The regression model is not statistically significant if its F-statistic and p-value are both low.
The estimated impact of each independent variable on the dependent variable, while maintaining the other variables constant, is represented by the coefficients. The regression equation in this situation would be as follows:
Dependent Variable = 0.16381 + 0.12976 * Variable 1 + 0.18573 * Variable 2 + 0.16405 * Variable 3 + 0.27308 * Variable 4 - 0.099852 * Variable 5
Therefore, the dependent variable can be predicted by including the intercept (0.16381) in addition to the weighted sum of all independent variables times their respective coefficients. The coefficient indicates the direction and magnitude of the effect of each independent variable on the dependent variable. For instance, if Independent Variable 4 grows by one unit, the dependent variable is anticipated to increase by 0.27308 units, with all other variables being constant. If Independent Variable 5 grows by one unit, the dependent variable is projected to decrease by 0.099852 units, all other variables remaining constant.
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Summary
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So what do you think about those values above ? which of of them has the great contribution or has more impact or has more influence to the dependent variable ?
Correct, Variabel 4 is more contribute to the denpendent value as it has a greatest coefficient value
Well Done ! see you in the next articles and practices.
-myresearchxpress
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