Multiple Linear Regression Analysis

In summary, multiple linear regression analysis is a statistical method used to analyze the relationship between a dependent variable and two or more independent variables. It is commonly used in fields such as economics, finance, and social sciences to make predictions about the dependent variable. The main assumptions of this method include linearity, normality, homoscedasticity, and independence of errors. Its accuracy can be evaluated using metrics such as R-squared, RMSE, and MAE. Some limitations of multiple linear regression analysis include its sensitivity to outliers, multicollinearity, and the assumption of linearity.
  • #1
Hotbirdym
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Hi,

I've asked this question on another forum, but no response until now. Maybe I will have a little bit of luck here. So .. I have a problem. I have a set of 8 parameter and I use this parameters in order to compute a measure (I vary each parameter with a step of 50%). I would like to know how these parameters influence the measure, which one has the highest loading on the measure that I must compute.
First I looked at PCA, but now I think this is not for my problem. Why? When I compute the correlation matrix I see that the correlation between parameters is almost 0 ( 1*pow(10, -20) ) which I consider to be 0. If the correlation is 0 then I tend to believe that they are independent so I need to use a different multivariate analysis method. Also, the correlation between each parameter and the measure is quite high, something like 0.50 or -0.70 and thus I conclude that they are high correlated. So I thought of using MLR. Am I right or not?
I think I have too many parameters and I've reduced the ones which have the lowest correlation with the measure (I've chosen the value for this parameters the highest - 100%) and now I have only 5 parameters.
Please correct me if I am wrong on choosing MLR method or suggest me another method to use in order to compute the influence each parameter has on my measure.

Many thanks,
Elena
 
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  • #2


Hello Elena,

Based on your description of your problem, it seems like using multiple linear regression (MLR) would be an appropriate method for determining the influence of each parameter on your measure. MLR is commonly used to analyze the relationship between multiple independent variables and a dependent variable, which seems to be the case in your situation.

However, it's important to keep in mind that MLR assumes that the independent variables are not highly correlated with each other. In your case, you mention that the correlation between each parameter and the measure is quite high, which may violate this assumption. In this case, you may want to consider using a different method, such as partial least squares regression (PLSR), which is better suited for analyzing highly correlated variables.

Another option could be to use principal component analysis (PCA) to reduce the number of parameters and then use MLR on the resulting principal components. This could help address the issue of high correlations between variables.

Overall, I would recommend trying out different methods and comparing their results to see which one best fits your data and research question. It's also important to thoroughly assess the assumptions and limitations of each method before making a decision. I hope this helps and good luck with your analysis!
 

1. What is multiple linear regression analysis?

Multiple linear regression analysis is a statistical method used to analyze the relationship between a dependent variable and two or more independent variables. It is used to predict the value of the dependent variable based on the values of the independent variables.

2. When is multiple linear regression analysis used?

Multiple linear regression analysis is commonly used when there is a need to understand the relationship between multiple variables and to make predictions about the dependent variable. It is often used in fields such as economics, finance, and social sciences.

3. What are the assumptions of multiple linear regression analysis?

The main assumptions of multiple linear regression analysis include linearity, normality, homoscedasticity, and independence of errors. Linearity assumes that there is a linear relationship between the dependent variable and the independent variables. Normality assumes that the errors are normally distributed. Homoscedasticity assumes that the variance of errors is constant for all values of the independent variables. Independence of errors assumes that there is no correlation between the errors.

4. How is the accuracy of a multiple linear regression model evaluated?

The accuracy of a multiple linear regression model can be evaluated using metrics such as the coefficient of determination (R-squared), root mean squared error (RMSE), and mean absolute error (MAE). R-squared measures the proportion of the variation in the dependent variable that can be explained by the independent variables. RMSE and MAE measure the difference between the actual values and the predicted values.

5. What are some limitations of multiple linear regression analysis?

Some limitations of multiple linear regression analysis include its sensitivity to outliers, multicollinearity, and the assumption of linearity. Outliers can significantly affect the results of the analysis and should be carefully examined. Multicollinearity, which occurs when the independent variables are highly correlated, can lead to unstable and unreliable estimates. The assumption of linearity may not hold true in some cases, and alternative regression methods may need to be used.

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