3003 Week 8 Practice Quiz

What is the primary purpose of using multiple regression analysis?

• To estimate a single mean response variable.

• To predict the value of one dependent variable based on the values of multiple independent variables

• To categorize data into distinct groups.

• To calculate correlation coefficients between variables.

Which assumption is not required in multiple regression analysis?

• Independence of errors.

• Normal distribution of variables.

• Homoscedasticity of errors.

• Equal variance across all levels of the independent variables.

What does multicollinearity refer to in the context of multiple regression?

• Correlation between error terms.

• A linear relationship between two or more independent variables.

• Correlation between the dependent and independent variables.

• The variance of the regression coefficients.

In the context of regression diagnostics, what is the purpose of a residual plot?

• To display the actual vs. predicted values of the dependent variable.

• To identify potential outliers in the data.

• To check the linearity and homoscedasticity of residuals.

• To compare different regression models.

Which of the following is an indication of a well-fitting regression model?

• High R-squared value.

• High standard error.

• Presence of multicollinearity.

• Presence of heteroscedasticity.

What is the implication of heteroscedasticity in a regression model?

• Increased standard errors of the coefficients, leading to less reliable statistical tests.

• Improved accuracy of the predictions.

• Reduced multicollinearity among predictors.

• Increased R-squared value.

Why might a researcher decide to apply a transformation to a variable in regression analysis?

• To make the data less understandable.

• To increase the multicollinearity between predictors.

• To make the data distribution more normal or stabilize variance, improving the validity of statistical tests.

• To reduce the computational speed of the analysis.

Which of the following transformations could be used to reduce right skewness in a data set?

• Squaring each data point.

• Taking the logarithm of each data point.

• Multiplying each data point by a constant.

• Adding a constant to each data point.

What does reflecting a variable involve in a statistical analysis?

• Rotating the data points around the median value.

• Multiplying the variable by -1 to change the direction of its effects.

• Dividing each data point by the maximum value.

• Shifting the mean of the variable to zero.

What is the Mahalanobis distance used for in multivariate data analysis?

• To measure the correlation between variables.

• To identify outliers in the data based on their distance from the center of the data set in terms of standard deviations.

• To calculate the Euclidean distance between points.

• To assess the linearity between variables.