Estimation in Simple Regression Model
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Questions and Answers

What is the primary purpose of the assumptions made for the regression model?

  • To make the regression analysis more computationally efficient
  • To ensure the regression coefficients are unbiased
  • To ensure the model fits the data well
  • To derive the stochastic properties of the OLS estimator (correct)
  • Which of the following assumptions is not required for the OLS estimator to be valid?

  • There is no multicollinearity between the explanatory variables (correct)
  • The error terms $u_i$ have a mean of zero conditional on the regressors $x_i$
  • The model $y_i = \beta_0 + \beta_1 x_i + u_i$ correctly describes the population regression function
  • The sample is a random sample from the population
  • Which of the following is a key property of the OLS estimator?

  • It is an unbiased estimator of the population regression coefficients
  • It has the smallest variance among all unbiased estimators
  • It follows a normal distribution
  • All of the above (correct)
  • What is the purpose of testing hypotheses regarding the population regression function using the OLS estimates?

    <p>To assess the statistical significance of the regression coefficients</p> Signup and view all the answers

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

    <p>The simple model has only one regressor, while the multiple model has multiple regressors</p> Signup and view all the answers

    Which of the following assumptions is not required for the OLS estimator to be unbiased?

    <p>The error terms $u_i$ have constant variance</p> Signup and view all the answers

    What is the main advantage of the multiple linear regression model over the simple linear regression model?

    <p>The multiple model can estimate the effects of multiple explanatory variables simultaneously</p> Signup and view all the answers

    Which of the following is NOT a property of the OLS estimator?

    <p>Normality</p> Signup and view all the answers

    How do experiments help with the assumptions of the regression model?

    <p>Experiments provide a random sample from the population</p> Signup and view all the answers

    What is the main interpretation of the regression coefficient $\beta_1$ in the simple linear regression model $y_i = \beta_0 + \beta_1 x_i + u_i$?

    <p>It represents the average change in $y_i$ for a one-unit increase in $x_i$, holding all other factors constant</p> Signup and view all the answers

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