Statistics Chapter 8

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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?

To identify the best-fitting line Signup and view all the answers

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

Because the positive and negative residuals cancel each other out Signup and view all the answers

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 Signup and view all the answers

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

α̂ + β̂Xi Signup and view all the answers

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 Signup and view all the answers

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

Residual Signup and view all the answers

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

Yi - Ŷi Signup and view all the answers

What is the relationship between ûi and ui?

ûi is the sample error term and ui is the population error term Signup and view all the answers

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

Ŷi = α̂ + β̂Xi Signup and view all the answers

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

To justify the conclusions drawn from the regression Signup and view all the answers

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

σ² Signup and view all the answers

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

No Bias Signup and view all the answers

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

Homoscedasticity Signup and view all the answers

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

5 Signup and view all the answers

What is the assumption about the model specification in regression?

We have the correct model specification Signup and view all the answers

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

The direction of the alternative hypothesis 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?

H0: β ≤ 0 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?

Use the column labeled '.05' to find the p-value Signup and view all the answers

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 Signup and view all the answers

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 Signup and view all the answers

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 Signup and view all the answers

What is the value of β in the null hypothesis?

Equal to 0 Signup and view all the answers

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

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

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

H0 : α = 0 Signup and view all the answers

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. Signup and view all the answers

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. 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?

Dividing the coefficient value by the standard error and seeing if that t-value passes the critical value. Signup and view all the answers