30 Questions
What is the main purpose of diagnostic checking in regression analysis?
To validate the regression model and check its assumptions
What is the role of residuals in regression analysis?
To estimate the deviations from the population regression line
Why do we need to check the conditions for regression inference?
To ensure that the regression model is a valid model
What is the purpose of plotting standardized residuals?
To validate the regression model and check its assumptions
What is the primary tool used to validate regression assumptions?
Plot of standardized residuals
What is the main goal of Aim 1 in regression analysis?
To critically assess the regression model
What is the main purpose of critically assessing the regression model?
To ensure the model meets the assumptions of linear regression
What is the primary goal of residual analysis in diagnostic checking?
To verify the assumption of constant variance
What is the assumption about the residuals in a simple linear regression model?
They have a zero mean and are normally distributed
What is the primary condition for making inferences about the regression model?
The residuals are normally distributed
What is the purpose of checking the conditions for regression inference?
To ensure the results of inference are reliable
What is the implication of the assumption of independence in a simple linear regression model?
The scatter about the true line will be Normally distributed
What does the slight curvature in the Normal probability plot of the residuals suggest?
The responses may not be Normally distributed about the line at each x-value.
Why should we not automatically eliminate outliers from the data?
Because outliers may be due to mistakes in data collection.
What is the purpose of influence analysis?
To determine the observations that have an influential effect on the fitted model.
What is the criteria used to determine if an observation is a leverage point?
If hi > 4/n, Xi is a leverage point.
What is the condition for an observation to be considered a candidate for removal from the model?
If Di > 4/n-2.
What is the purpose of using multiple criteria, such as the hat matrix elements, Studentized deleted residuals, and Cook's distance statistic, in influence analysis?
To ensure that only when all three criteria provide consistent results, an observation should be removed.
What is the primary purpose of the influence.measures function in R?
To explore measures of leverage and Cook's distance
What is a bad leverage point?
A point whose standardized residual falls outside the interval from –2 to 2
What is the purpose of the smoothing red curves in the plot(prod.lm) output in R?
To help identify patterns
What is an outlier in the context of regression analysis?
A point whose standardized residual falls outside the interval from –2 to 2
What is the characteristic of a good leverage point?
Its standardized residual falls inside the interval from –4 to 4 for large sample size
What is the condition for normality to be satisfied in a regression analysis?
The data should have a fairly constant spread
What is the primary characteristic of a US Treasury bond that makes it a safe investment?
Government backing
What is the effect of a 1% increase in the coupon rate on the mean bid price, according to the fitted model?
$3.07 increase
What is the purpose of plotting standardized residuals?
To identify influential points
Why are the three points on the left in the plot of the data dragging the least squares line away from the bulk of the points?
They have high leverage
What is the recommended approach to deal with influential points in the data?
Remove them and re-fit the model
What is the interval estimate for the slope of the least squares line?
(2.44, 3.69)
This quiz covers the topics of critically assessing the regression model, diagnostic checking, and transformation in the context of analysis of experiments. It reviews the simple linear regression model, assumptions, and residual analysis.
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