Unit I Modeling For Data Science

Which of the following is a goal of statistical modeling?

• A) Identifying patterns in data

• B) Making predictions
  

• C) Understanding relationships between variables
  

• D) All of the above
  

The linear regression model assumes which of the following?

• A) Non-linearity
  

• B) Homoscedasticity
  

• C) Multicollinearity
  

• D) None of the above
  

The matrix representation of a linear regression model is Y=Xβ+ϵ

• True

• False

Which of the following best describes the assumption of concept validity?

• A) The model is mathematically correct
  

• B) The concepts in the model accurately represent real-world phenomena
  

• C) The data is normally distributed
  

• D) The variables are independent
  

Linear regression is most appropriate when the relationship between the independent and dependent variables is:

• A) Non-linear
  

• B) Curvilinear
  

• C) Linear
  

• D) Exponential
  

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

• A) The errors are normally distributed
  

• B) The relationship between the independent and dependent variables is linear
  

• C) The dependent variable is categorical
  

• D) The variance of errors is constant across observations
  

The matrix representation of the linear regression model simplifies the computation of multiple regression coefficients.

• True

• False

What does the term "homoscedasticity" refer to in the context of linear regression?

• A) The errors are independent of each other
  

• B) The variance of errors is constant
  

• C) The model fits the data perfectly
  

• D) The predictors are uncorrelated
  

Which of the following is a potential issue if linear regression assumptions are violated?

• A) Biased estimators
  

• B) Inflated standard errors
  

• C) Invalid statistical inference
  

• D) All of the above
  

In the context of linear regression, what is the role of the error term (ϵ\epsilonϵ) in the model Y=β0+β1X+ϵ

• A) It captures the random noise or deviations from the linear relationship
  

• B) It represents the slope of the regression line
  

• C) It defines the intercept of the regression model
  

• D) It measures the goodness-of-fit of the model