Question

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1. What is the purpose of saying “all-else-equal” or “ceteris paribus” when it comes to multiple linear regression?
2. Why is the F-test important in multiple linear regression more so than in simple linear regression?
3. What is the difference between the AIC and BIC?
4. Why is outlier analysis so important?
5. What is the danger in using stepwise regression?
6. What is the difference between Cook’s Distance and DFFITS?
7. What can you do to remove multicollinearity?
8. What is a VIF?
9. If you have to create dummy variables for the seven continents of the world, how many columns do you create and why?
10. Why do we standardize residuals?
11. Describe a QQ plot and what it can tell us.

Answer 1

1. What is the purpose of saying “all-else-equal” or “ceteris paribus” when it comes to multiple linear regression?

Ceteris paribus is latin and means the others equal, i.e. all other variables fixed.  In context, this means: keeping all other variables fixed.

Multiple linear regression analysis is an extension of simple linear regression analysis, used to assess the association between two or more independent variables and a single continuous dependent variable. The multiple linear regression equation is as follows:

,

whereis the predicted or expected value of the dependent variable, X1 through Xp are p distinct independent or predictor variables, b0 is the value of Y when all of the independent variables (X1 through Xp) are equal to zero, and b1 through bp are the estimated regression coefficients. Each regression coefficient represents the change in Y relative to a one unit change in the respective independent variable. In the multiple regression situation, b1, for example, is the change in Y relative to a one unit change in X1, holding all other independent variables constant (i.e., when the remaining independent variables are held at the same value or are fixed).

2. Why is the F-test important in multiple linear regression more so than in simple linear regression?

F-test in regression compares the fits of different linear models. Unlike t-tests that can assess only one regression coefficient at a time, the F-test can assess multiple coefficients simultaneously. The F-test of the overall significance is a specific form of the F-test. It compares a model with no predictors to the model that you specify.

3. What is the difference between the AIC and BIC?

AIC and BIC are widely used in model selection criteria. AIC means Akaike’s Information Criteria and BIC means Bayesian Information Criteria. Though these two terms address model selection, they are not the same. One can come across may difference between the two approaches of model selection.The AIC can be termed as a mesaure of the goodness of fit of any estimated statistical model. The BIC is a type of model selection among a class of parametric models with different numbers of parameters.

Akaike’s Information Criteria generally tries to find unknown model that has high dimensional reality. This means the models are not true models in AIC. On the other hand, the Bayesian Information Criteria comes across only True models. It can also be said that Bayesian Information Criteria is consistent whereas Akaike’s Information Criteria is not so. When Akaike’s Information Criteria will present the danger that it would outfit. the Bayesian Information Criteria will present the danger that it would underfit. Though BIC is more tolerant when compared to AIC, it shows less tolerance at higher numbers.

4. Why is outlier analysis so important?

Outliers can range from being unimportant to being really important.

• Outliers are unimportant if they capture inaccurate information, and/or if they carry little weight in the analysis.
• Outliers are really important if they carry a lot of weight, and/or if they give you important information that the more “normal” data don’t.

If it can be determined that an outlying point is in fact erroneous, then the outlying value should be deleted from the analysis (or corrected if possible).

In some cases, it may not be possible to determine if an outlying point is bad data. Outliers may be due to random variation or may indicate something scientifically interesting. In any event, we should not simply delete the outlying observation before a through investigation. In running experimdnts , we may repeat the experiment. If the data contains significant outliers, we may need to consider the use of robust statistical techniques.

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