CHAPTER 2 OPEN QUESTIONS
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Catégorie :Category: nCreator TI-Nspire
Auteur Author: SPITZER2001
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Mis en ligne Uploaded: 05/05/2025 - 21:18:34
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Shortlink : https://tipla.net/a4620859
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 5.90 Ko KB
Mis en ligne Uploaded: 05/05/2025 - 21:18:34
Uploadeur Uploader: SPITZER2001 (Profil)
Téléchargements Downloads: 7
Visibilité Visibility: Archive publique
Shortlink : https://tipla.net/a4620859
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Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
<<
What is regression analysis and what are its main goals? Answer: Regression analysis is a statistical technique used to model and analyze the relationship between a dependent variable and one or more independent variables. The main goals are to predict the dependent variable, assess relationships, and understand underlying trends in the data. What is the difference between simple linear regression and multiple linear regression? Answer: Simple linear regression involves modeling the relationship between a single independent variable and the dependent variable using a straight line. Multiple linear regression involves two or more independent variables and fits a hyperplane to the data. What is the meaning of the coefficients in a linear regression model? Answer: The coefficients represent the slope (for continuous variables) or the effect of each independent variable on the dependent variable. The intercept represents the predicted value of the dependent variable when all independent variables are zero. How do you interpret R-squared in a regression model? Answer: R-squared measures the proportion of the variance in the dependent variable that is explained by the independent variables in the model. It ranges from 0 to 1, where a higher value indicates a better fit of the model to the data. What is the assumption of homoscedasticity in regression analysis? Answer: Homoscedasticity assumes that the variance of the errors (residuals) is constant across all levels of the independent variables. If this assumption is violated (heteroscedasticity), it may lead to inefficient estimates and biased statistical tests. What is multicollinearity, and how does it affect regression analysis? Answer: Multicollinearity occurs when independent variables in a regression model are highly correlated with each other. This can lead to unreliable estimates of the regression coefficients, making it difficult to determine the individual effect of each predictor. What is the difference between R-squared and adjusted R-squared? Answer: R-squared measures the proportion of variance explained by the model, but it can increase with more predictors, even if those predictors do not improve the model. Adjusted R-squared adjusts for the number of predictors, providing a more accurate measure of model fit when multiple predictors are used. What is regularization in regression, and why is it important? Answer: Regularization is a technique used to prevent overfitting by adding a penalty term to the regression model. It discourages the use of large coefficients by shrinking them toward zero, improving the model's ability to generalize to new data. Common forms are Lasso (L1) and Ridge (L2) regularization. What is the difference between Lasso and Ridge regression? Answer: Lasso regression uses L1 regularization, which encourages sparsity in the model by driving some coefficients to exactly zero, effectively performing feature selection. Ridge regression uses L2 regularization, which shrinks coefficients but does not set them exactly to zero, making it better for handling multicollinearity. What is the meaning of residuals in regression, and how are they used? Answer: Residuals are the differences between the observed values and the predicted values in a regression model. They are used to assess the fit of the model, check for violations of assumptions (like homoscedasticity or normality), and diagnose potential problems such as outliers or model mis-specification. How can you check for multicollinearity in a regression model? Answer: Multicollinearity can be checked using the Variance Inflation Factor (VIF), which quantifies how much the variance of the estimated regression coefficients is inflated due to multicollinearity. A high VIF indicates high multicollinearity. Explain the concept of bias and variance in regression analysis. Answer: Bias refers to the error introduced by approximating a real-world problem with a simplified model. Variance refers to the error introduced by sensitivity to small fluctuations in the training data. A good model minimizes both bias and variance, achieving a balance between underfitting and overfitting. What is the purpose of cross-validation in regression? Answer: Cross-validation is used to assess the performance of a regression model on different subsets of the data to ensure that it generalizes well to unseen data. It helps in detecting overfitting and underfitting and gives a more reliable estimate of model accuracy. What is the effect of outliers on a regression model? Answer: Outliers can distort the results of a regression model by exerting undue influence on the estimated coefficients, leading to biased predictions and unreliable conclusions. Robust regression techniques can be used to minimize the effect of outliers. Explain the concept of p-value in regression analysis. Answer: The p-value measures the strength of evidence against the null hypothesis in statistical tests. In regression, it indicates wh
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>>
Compatible OS 3.0 et ultérieurs.
<<
What is regression analysis and what are its main goals? Answer: Regression analysis is a statistical technique used to model and analyze the relationship between a dependent variable and one or more independent variables. The main goals are to predict the dependent variable, assess relationships, and understand underlying trends in the data. What is the difference between simple linear regression and multiple linear regression? Answer: Simple linear regression involves modeling the relationship between a single independent variable and the dependent variable using a straight line. Multiple linear regression involves two or more independent variables and fits a hyperplane to the data. What is the meaning of the coefficients in a linear regression model? Answer: The coefficients represent the slope (for continuous variables) or the effect of each independent variable on the dependent variable. The intercept represents the predicted value of the dependent variable when all independent variables are zero. How do you interpret R-squared in a regression model? Answer: R-squared measures the proportion of the variance in the dependent variable that is explained by the independent variables in the model. It ranges from 0 to 1, where a higher value indicates a better fit of the model to the data. What is the assumption of homoscedasticity in regression analysis? Answer: Homoscedasticity assumes that the variance of the errors (residuals) is constant across all levels of the independent variables. If this assumption is violated (heteroscedasticity), it may lead to inefficient estimates and biased statistical tests. What is multicollinearity, and how does it affect regression analysis? Answer: Multicollinearity occurs when independent variables in a regression model are highly correlated with each other. This can lead to unreliable estimates of the regression coefficients, making it difficult to determine the individual effect of each predictor. What is the difference between R-squared and adjusted R-squared? Answer: R-squared measures the proportion of variance explained by the model, but it can increase with more predictors, even if those predictors do not improve the model. Adjusted R-squared adjusts for the number of predictors, providing a more accurate measure of model fit when multiple predictors are used. What is regularization in regression, and why is it important? Answer: Regularization is a technique used to prevent overfitting by adding a penalty term to the regression model. It discourages the use of large coefficients by shrinking them toward zero, improving the model's ability to generalize to new data. Common forms are Lasso (L1) and Ridge (L2) regularization. What is the difference between Lasso and Ridge regression? Answer: Lasso regression uses L1 regularization, which encourages sparsity in the model by driving some coefficients to exactly zero, effectively performing feature selection. Ridge regression uses L2 regularization, which shrinks coefficients but does not set them exactly to zero, making it better for handling multicollinearity. What is the meaning of residuals in regression, and how are they used? Answer: Residuals are the differences between the observed values and the predicted values in a regression model. They are used to assess the fit of the model, check for violations of assumptions (like homoscedasticity or normality), and diagnose potential problems such as outliers or model mis-specification. How can you check for multicollinearity in a regression model? Answer: Multicollinearity can be checked using the Variance Inflation Factor (VIF), which quantifies how much the variance of the estimated regression coefficients is inflated due to multicollinearity. A high VIF indicates high multicollinearity. Explain the concept of bias and variance in regression analysis. Answer: Bias refers to the error introduced by approximating a real-world problem with a simplified model. Variance refers to the error introduced by sensitivity to small fluctuations in the training data. A good model minimizes both bias and variance, achieving a balance between underfitting and overfitting. What is the purpose of cross-validation in regression? Answer: Cross-validation is used to assess the performance of a regression model on different subsets of the data to ensure that it generalizes well to unseen data. It helps in detecting overfitting and underfitting and gives a more reliable estimate of model accuracy. What is the effect of outliers on a regression model? Answer: Outliers can distort the results of a regression model by exerting undue influence on the estimated coefficients, leading to biased predictions and unreliable conclusions. Robust regression techniques can be used to minimize the effect of outliers. Explain the concept of p-value in regression analysis. Answer: The p-value measures the strength of evidence against the null hypothesis in statistical tests. In regression, it indicates wh
[...]
>>
