Statistics Chapter 8
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Questions and Answers

What is the main goal when estimating a regression line?

  • To identify the correlation coefficient
  • To draw a line that comes as close as possible to the cases in the scatter plot (correct)
  • To predict the exact value of the dependent variable
  • To explain the relationship between the dependent and independent variables

Why can't we simply add up the residual values to summarize the fit of each line?

  • Because residual values are not measurable
  • Because residual values are always positive
  • Because positive and negative residual values cancel each other out (correct)
  • Because residual values are always negative

What do we want to minimize when estimating a regression line?

  • The slope of the line
  • The intercept of the line
  • The correlation coefficient
  • The residual values (correct)

What is the purpose of assessing the fit of each line?

<p>To identify the best-fitting line (D)</p> Signup and view all the answers

Why do we need a method to assess the fit of each line?

<p>Because the positive and negative residuals cancel each other out (B)</p> Signup and view all the answers

What do we want to achieve when drawing a regression line?

<p>To draw a line that comes as close as possible to the cases in the scatter plot (B)</p> Signup and view all the answers

What is the predicted value of Yi calculated using α̂ and β̂?

<p>α̂ + β̂Xi (A)</p> Signup and view all the answers

What does the residual (ûi) represent in the context of a two-variable regression model?

<p>The difference between the actual and predicted values of the dependent variable (B)</p> Signup and view all the answers

What is another name for the estimated stochastic component (ûi)?

<p>Residual (D)</p> Signup and view all the answers

What is the formula for calculating the residual (ûi)?

<p>Yi - YÌ‚i (A)</p> Signup and view all the answers

What is the relationship between ûi and ui?

<p>ûi is the sample error term and ui is the population error term (C)</p> Signup and view all the answers

What is the equation for the two-variable regression model?

<p>Ŷi = α̂ + β̂Xi (D)</p> Signup and view all the answers

What is the primary reason for making assumptions about the population stochastic component in regression?

<p>To justify the conclusions drawn from the regression (A)</p> Signup and view all the answers

What is the symbol for the variance of the population stochastic component in the given notation?

<p>σ² (B)</p> Signup and view all the answers

What is the assumption that the mean of the population stochastic component is equal to zero?

<p>No Bias (D)</p> Signup and view all the answers

What is the term for the assumption that the variance of the population stochastic component is constant?

<p>Homoscedasticity (A)</p> Signup and view all the answers

How many assumptions are made about the population stochastic component in regression?

<p>5 (B)</p> Signup and view all the answers

What is the assumption about the model specification in regression?

<p>We have the correct model specification (D)</p> Signup and view all the answers

What is the primary difference between a one-tailed hypothesis test and a two-tailed hypothesis test?

<p>The direction of the alternative hypothesis (B)</p> Signup and view all the answers

What is the null hypothesis in a one-tailed test, where the alternative hypothesis is that the parameter is positive?

<p>H0: β ≤ 0 (D)</p> Signup and view all the answers

How do you use the t-table in Appendix B to get the right p-value for a one-tailed test?

<p>Use the column labeled '.05' to find the p-value (A)</p> Signup and view all the answers

What is the purpose of the t-ratio calculation in a one-tailed hypothesis test?

<p>To test which of the two rival hypotheses is supported (C)</p> Signup and view all the answers

Can one-tailed tests be used on the intercept (α) in a regression model?

<p>Yes, and the calculation is the same as for the slope (B)</p> Signup and view all the answers

What is the reason for using a one-tailed hypothesis test instead of a two-tailed hypothesis test?

<p>The theory predicts the direction of the relationship (C)</p> Signup and view all the answers

What is the value of β in the null hypothesis?

<p>Equal to 0 (D)</p> Signup and view all the answers

What is the formula used to test hypotheses about the y-intercept parameter?

<p>tn−k = α̂−α∗ / se(α̂) (A)</p> Signup and view all the answers

What is the null hypothesis in the context of testing the y-intercept parameter?

<p>H0 : α = 0 (D)</p> Signup and view all the answers

What is the relationship between the 95% confidence interval and a two-tailed hypothesis test?

<p>If the 95% confidence interval does not include a particular value, then the null hypothesis that the population equals that value will have a p-value smaller than 0.05. (B)</p> Signup and view all the answers

What can be concluded if the 95% confidence interval for a particular parameter does not include zero?

<p>The null hypothesis that the population equals zero will have a p-value smaller than 0.05. (A)</p> Signup and view all the answers

When evaluating whether a null hypothesis is that a coefficient value equals zero, what is the calculation being performed?

<p>Dividing the coefficient value by the standard error and seeing if that t-value passes the critical value. (B)</p> Signup and view all the answers

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