30 Questions
What is the main goal when estimating a regression line?
To draw a line that comes as close as possible to the cases in the scatter plot
Why can't we simply add up the residual values to summarize the fit of each line?
Because positive and negative residual values cancel each other out
What do we want to minimize when estimating a regression line?
The residual values
What is the purpose of assessing the fit of each line?
To identify the best-fitting line
Why do we need a method to assess the fit of each line?
Because the positive and negative residuals cancel each other out
What do we want to achieve when drawing a regression line?
To draw a line that comes as close as possible to the cases in the scatter plot
What is the predicted value of Yi calculated using α̂ and β̂?
α̂ + β̂Xi
What does the residual (ûi) represent in the context of a two-variable regression model?
The difference between the actual and predicted values of the dependent variable
What is another name for the estimated stochastic component (ûi)?
Residual
What is the formula for calculating the residual (ûi)?
Yi - Ŷi
What is the relationship between ûi and ui?
ûi is the sample error term and ui is the population error term
What is the equation for the two-variable regression model?
Ŷi = α̂ + β̂Xi
What is the primary reason for making assumptions about the population stochastic component in regression?
To justify the conclusions drawn from the regression
What is the symbol for the variance of the population stochastic component in the given notation?
σ²
What is the assumption that the mean of the population stochastic component is equal to zero?
No Bias
What is the term for the assumption that the variance of the population stochastic component is constant?
Homoscedasticity
How many assumptions are made about the population stochastic component in regression?
5
What is the assumption about the model specification in regression?
We have the correct model specification
What is the primary difference between a one-tailed hypothesis test and a two-tailed hypothesis test?
The direction of the alternative hypothesis
What is the null hypothesis in a one-tailed test, where the alternative hypothesis is that the parameter is positive?
H0: β ≤ 0
How do you use the t-table in Appendix B to get the right p-value for a one-tailed test?
Use the column labeled '.05' to find the p-value
What is the purpose of the t-ratio calculation in a one-tailed hypothesis test?
To test which of the two rival hypotheses is supported
Can one-tailed tests be used on the intercept (α) in a regression model?
Yes, and the calculation is the same as for the slope
What is the reason for using a one-tailed hypothesis test instead of a two-tailed hypothesis test?
The theory predicts the direction of the relationship
What is the value of β in the null hypothesis?
Equal to 0
What is the formula used to test hypotheses about the y-intercept parameter?
tn−k = α̂−α∗ / se(α̂)
What is the null hypothesis in the context of testing the y-intercept parameter?
H0 : α = 0
What is the relationship between the 95% confidence interval and a two-tailed hypothesis test?
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.
What can be concluded if the 95% confidence interval for a particular parameter does not include zero?
The null hypothesis that the population equals zero will have a p-value smaller than 0.05.
When evaluating whether a null hypothesis is that a coefficient value equals zero, what is the calculation being performed?
Dividing the coefficient value by the standard error and seeing if that t-value passes the critical value.
This quiz covers the concepts of simple linear regression, predicted values, and residuals in statistical analysis. It includes equations and formulas for calculating predicted values and residuals.
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