Data Science Lecture 8

In simple linear regression, what is the relationship being modeled?

Between one dependent and one independent variable

What does the slope in a simple linear regression represent?

The average change in the dependent variable for a one-unit change in the independent variable

Which method is commonly used to estimate the coefficients in simple linear regression?

Least Squares

What assumption is made about the error terms in simple linear regression?

They are normally distributed with constant variance

Which metric measures the proportion of variation in the dependent variable explained by the independent variable?

R-squared

What is the range of the R-squared statistic in simple linear regression?

0 to 1

Which of the following indicates a perfect linear relationship?

R² = 1

If the slope coefficient is not significantly different from zero, what does that imply?

The independent variable has no linear relationship with the dependent variable

What does the residual in a regression model represent?

The error between the observed and predicted value

Which of the following assumptions is violated when there is heteroscedasticity?

Constant variance of residuals

Which diagnostic plot helps assess the linearity assumption?

Residuals vs Fitted plot

In simple linear regression, the total sum of squares (TSS) is equal to:

Regression sum of squares + Residual sum of squares

Which of the following is not an assumption of simple linear regression?

No multicollinearity

Which of the following tests whether the slope is significantly different from zero?

t-test

When the slope is negative, the relationship between X and Y is:

Inverse

What does the intercept () represent in a simple linear regression?

The predicted value of Y when X is 0

Which condition indicates a potential outlier in simple linear regression?

High leverage or large standardized residual

What does Mean Squared Error (MSE) measure in linear regression?

Average of squared residuals

Which metric is used to determine how well a regression model fits unseen data?

RMSE on validation/test data

What distinguishes multiple linear regression from simple linear regression?

It includes more than one independent variable

Which method is commonly used to estimate the parameters in multiple linear regression?

Least Squares

What does the R-squared value represent in multiple linear regression?

The proportion of variance in Y explained by all predictors

What is the range of the R-squared statistic?

0 to 1

Which of the following is a key assumption of multiple linear regression?

Errors have constant variance (homoscedasticity)

What does multicollinearity refer to in multiple regression?

Correlation among independent variables

Which statistic is used to detect multicollinearity?

Variance Inflation Factor (VIF)

Which of the following indicates serious multicollinearity?

VIF > 10

Which test is used to assess the overall significance of a multiple regression model?

F-test

What does the coefficient of an independent variable represent in multiple regression?

The effect of the variable controlling for others

What does a small p-value for a predictor indicate?

There is strong evidence against the null hypothesis

What does the error term in the regression model account for?

Unexplained variation in Y

Which of the following plots is used to diagnose homoscedasticity?

Residuals vs Fitted

Which of the following is a consequence of multicollinearity?

Inflated standard errors

Which selection method starts with no predictors and adds one at a time?

Forward selection

Which selection method removes the least significant predictor at each step?

Backward elimination

Which of the following is NOT an assumption of classical linear regression?

Normality of predictors

What assumption is violated if residuals show a funnel shape when plotted against fitted values?

Homoscedasticity

Which assumption is checked using a Q-Q plot of residuals?

Normality of residuals

Which of the following best indicates multicollinearity?

VIF > 10 for one or more predictors

Violation of the normality assumption primarily affects:

Confidence intervals and hypothesis tests

Which of the following indicates a violation of the linearity assumption?

Residuals vs Fitted plot has a curved shape

What is the main consequence of heteroscedasticity?

Invalid standard errors and inference

Which of the following is most likely to reduce the effect of multicollinearity?

Use Ridge regression

Which type of plot is most useful to diagnose violations of the homoscedasticity assumption?

Residuals vs Fitted values

What does a high VIF value indicate?

Multicollinearity

If residuals are not independent, what assumption is violated?

Independence of errors

Which transformation might correct non-linearity in predictors?

Logarithmic transformation

Which assumption violation is most likely when time-series data is used without controlling for time effects?

Autocorrelation

If residuals have increasing variance as fitted values increase, this indicates:

Heteroscedasticity

Which regression technique helps to handle multicollinearity?

Ridge regression

The consequence of multicollinearity in a regression model is:

Inflated standard errors and unstable coefficients

Which metric measures the square root of the average of squared residuals?

RMSE

What does the Mean Absolute Error (MAE) measure in a linear regression model?

Average of absolute residuals

Which performance metric penalizes large errors more heavily than small ones?

RMSE

Which criterion is used to compare linear regression models by balancing fit and complexity?

AIC (Akaike Information Criterion)

What is the main drawback of using R-squared as the only performance measure?

It never decreases with added predictors

Which of the following measures is scale-dependent and cannot be compared across datasets?

RMSE

What is the difference between AIC and BIC in model selection?

BIC imposes a higher penalty for model complexity

Which metric measures prediction accuracy as a percentage?

MAPE (Mean Absolute Percentage Error)

When using cross-validation for linear regression, which measure is typically used to assess prediction error?

Cross-validated RMSE

Which performance metric increases if the residuals become more variable?

RMSE

Which of the following indicates poor model generalization on unseen data?

Low training RMSE and high validation RMSE

Which measure is suitable for evaluating models with different numbers of predictors and sample sizes?

Adjusted R-squared

If two models have similar AIC values, which should be preferred?

The one with fewer predictors

Which measure combines both bias and variance in its calculation?

RMSE

Which tool is most commonly used to detect multicollinearity in multiple linear regression?

VIF (Variance Inflation Factor)

What does a VIF value greater than 10 usually suggest?

Strong multicollinearity

Which plot is best for checking homoscedasticity?

Residuals vs Fitted plot

A curved pattern in the Residuals vs Fitted plot indicates a violation of:

Linearity

The Durbin-Watson test is used to detect:

Autocorrelation

A Q-Q plot that deviates from a straight line indicates a violation of:

Normality of residuals

Which of the following suggests heteroscedasticity in a residuals vs fitted plot?

Funnel-shaped spread

Which of the following graphical tools can be used to identify observations with unusually large or small residuals in a linear regression model?

Boxplot of residuals

What assumption is violated if residuals are positively autocorrelated?

Independence of errors

If predictors are highly correlated, which consequence is most likely?

Inflated standard errors

A histogram of residuals is primarily used to assess which assumption?

Normality

The Box-Cox transformation is often applied when which assumption is violated?

Normality or constant variance

When is stepwise regression useful in the context of assumption checks?

To reduce multicollinearity by removing redundant predictors

Which is NOT a proper method to detect multicollinearity?

Residuals vs fitted plot

What assumption is likely violated if the residuals are not symmetrically distributed?

Normality