Correlation and Regression Analysis

Question 1

What does correlation measure in statistics?

Answer 1

Correlation measures the strength and direction of the relationship between two variables.

Question 2

Explain the difference between positive and negative correlation.

Answer 2

Positive correlation means that as one variable increases, the other also tends to increase, while negative correlation means that as one variable increases, the other tends to decrease.

Question 3

How is the strength of correlation determined?

Answer 3

The strength of correlation is determined by the absolute value of the correlation coefficient, with values closer to 1 indicating stronger correlation.

Question 4

What does a correlation coefficient of 0 indicate?

Answer 4

A correlation coefficient of 0 indicates no linear relationship between the variables.

Question 5

What is the range of values for the Pearson correlation coefficient?

Answer 5

The range of values for the Pearson correlation coefficient is -1 to 1.

Question 6

When should you use Spearman’s rank correlation coefficient instead of Pearson’s?

Answer 6

Spearman’s rank correlation coefficient is used when the relationship between variables is not linear or when the data are ordinal.

Question 7

Describe the process of linear regression analysis.

Answer 7

Linear regression analysis involves fitting a straight line to the data points to model the relationship between a dependent variable and one or more independent variables.

Question 8

What is the difference between simple linear regression and multiple linear regression?

Answer 8

Simple linear regression involves one independent variable, while multiple linear regression involves two or more independent variables.

Question 9

How do you interpret the slope coefficient in regression analysis?

Answer 9

The slope coefficient represents the change in the dependent variable for a one-unit change in the independent variable.

Question 10

What does the intercept term represent in a regression equation?

Answer 10

The intercept term represents the value of the dependent variable when all independent variables are set to zero.

Question 11

What assumptions must be met for regression analysis?

Answer 11

Assumptions include linearity, independence of errors, homoscedasticity, and normality of errors.

Question 12

What is the purpose of residual analysis in regression?

Answer 12

Residual analysis involves examining the differences between observed and predicted values to assess the model’s performance.

Question 13

What are influential points in regression analysis?

Answer 13

Influential points are data points that have a large impact on the regression coefficients and may significantly alter the results.

Question 14

How do you assess the goodness of fit in regression analysis?

Answer 14

Goodness of fit is assessed using measures like R-squared, which indicates the proportion of variance in the dependent variable explained by the independent variables.

Question 15

What is multicollinearity, and why is it problematic in regression?

Answer 15

Multicollinearity occurs when independent variables in a regression model are highly correlated, leading to unreliable estimates of regression coefficients.

Question 16

Explain the concept of homoscedasticity in regression analysis.

Answer 16

Homoscedasticity means that the variance of the errors is constant across all levels of the independent variables.

Question 17

What is autocorrelation, and how does it affect regression analysis?

Answer 17

Autocorrelation occurs when errors in a regression model are correlated with each other, violating the assumption of independence of errors.

Question 18

What is heteroscedasticity, and how does it differ from homoscedasticity?

Answer 18

Heteroscedasticity means that the variance of the errors is not constant across all levels of the independent variables.

Question 19

When should you use logistic regression instead of linear regression?

Answer 19

Logistic regression is used when the dependent variable is binary or categorical.

Question 20

What is the purpose of diagnostic plots in regression analysis?

Answer 20

Diagnostic plots help identify potential problems with the regression model, such as non-linearity or heteroscedasticity.

Question 21

How do you detect outliers in regression analysis?

Answer 21

Outliers can be detected by examining residual plots or leverage statistics.

Question 22

What are the assumptions of logistic regression?

Answer 22

Assumptions include linearity of the logit, independence of observations, absence of multicollinearity, and absence of influential points.

Question 23

How do you interpret odds ratios in logistic regression?

Answer 23

Odds ratios represent the change in odds of the dependent variable for a one-unit change in the independent variable.

Question 24

What is the Akaike Information Criterion (AIC), and how is it used in regression analysis?

Answer 24

AIC is a measure of the relative quality of statistical models, with lower values indicating better fit.

Question 25

What is stepwise regression, and when is it appropriate?

Answer 25

Stepwise regression is a method for selecting the most important independent variables for inclusion in a regression model.

Question 26

How does regularization help improve regression models?

Answer 26

Regularization helps prevent overfitting by penalizing large coefficients in regression models.

Question 27

What is the purpose of cross-validation in regression analysis?

Answer 27

Cross-validation is used to evaluate the performance of a regression model on unseen data.

Question 28

What are the limitations of regression analysis?

Answer 28

Limitations include the assumption of linearity, sensitivity to outliers, and potential violations of regression assumptions.

Question 29

How can you assess the linearity assumption in regression?

Answer 29

Linearity assumption can be assessed using scatter plots or residual plots.

Question 30

Explain the difference between correlation and causation.

Answer 30

Correlation indicates a relationship between variables, while causation implies that one variable directly influences the other.

Question 31

What is a dummy variable, and how is it used in regression analysis?

Answer 31

A dummy variable is a binary variable used to represent categories in regression analysis.

Question 32

How do you handle missing data in regression analysis?

Answer 32

Missing data can be handled using methods like imputation or excluding incomplete cases.

Question 33

What is the difference between a parametric and a non-parametric regression model?

Answer 33

Parametric regression models assume a specific form for the relationship between variables, while non-parametric models do not.

Question 34

How do you interpret R-squared in regression analysis?

Answer 34

R-squared represents the proportion of variance in the dependent variable explained by the independent variables.

Question 35

What is the difference between prediction and inference in regression analysis?

Answer 35

Prediction involves estimating future outcomes based on the model, while inference involves understanding the relationship between variables.

Question 36

What is the Durbin-Watson statistic, and what does it indicate?

Answer 36

Durbin-Watson statistic tests for the presence of autocorrelation in the residuals, with values close to 2 indicating no autocorrelation.

Question 37

How do you handle multicollinearity in regression analysis?

Answer 37

Multicollinearity can be handled by removing one of the correlated variables or by using techniques like principal component analysis.

Question 38

What is the purpose of interaction terms in regression?

Answer 38

Interaction terms allow for the examination of how the relationship between two variables changes depending on the value of a third variable.

Question 39

Why is it important to check for normality in regression residuals?

Answer 39

Checking for normality in regression residuals ensures that the assumption of normally distributed errors is met.

Question 40

What are the assumptions of robust regression?

Answer 40

Assumptions of robust regression include linearity, independence of errors, and homoscedasticity, but it is less sensitive to violations of these assumptions.

Question 41

How do you assess the model's predictive performance in regression analysis?

Answer 41

The model's predictive performance can be assessed using metrics like mean squared error or cross-validated R-squared.

Question 42

What is the role of feature selection in regression modeling?

Answer 42

Feature selection involves choosing the most relevant independent variables for inclusion in the regression model.