Regression Analysis Homework: Best Model & Appropriateness

[david118]

Homework Statement

based on this data
http://www.stat.ufl.edu/~rrandles/sta4210/4210lectures/secondexreview/exam2rev.pdf

1) Consider the full (three predictor) model. Is this model useful? (are any of the predictors worthwhile?)

2) Use the All-Subsets and conduct a search for the best model using our five criteria.

3) Examine the approprateness of the model chosen in 2.

4) Conduct a test of whether X2 - (locadv) should be dropped from the three variable model.

Homework Equations

The Attempt at a Solution

So,
1) I would say the model is useful based upon the fact that the F-Value in the anova test is larger than the one on the F-table based upon the degrees of freedom.

2) According the all-subsets data, the best model uses X1 and X3

3)Since the F-test is greater than slated F-table value, it is appropriate. (NOT SURE ABOUT THIS PART)

4) Since the model is better than the all three, that variable should be dropped. (NOT SURE ABOUT THIS)

thanks

 

[nate808]

for your post! Here is my response to your questions:

1) Based on the data provided, it does appear that the full (three predictor) model is useful. The F-value in the ANOVA test is larger than the one on the F-table, indicating that at least one of the predictors is having a significant effect on the outcome. However, we cannot determine which specific predictors are worthwhile without further analysis.

2) To determine the best model, we can use the All-Subsets method and conduct a search using the five criteria (e.g. adjusted R-squared, AIC, BIC, etc.). This will allow us to compare different models and select the one that best fits the data.

3) The appropriateness of the model chosen in 2 will depend on the criteria used to select it. If the chosen model has a high adjusted R-squared and low AIC and BIC values, then it can be considered appropriate. However, it is important to also consider the assumptions of the model and whether they are being met.

4) To determine if X2 - (locadv) should be dropped from the three variable model, we can conduct a test such as a t-test or F-test to assess if the coefficient for this predictor is significantly different from zero. If the p-value for this test is less than the chosen significance level (e.g. 0.05), then we can conclude that this predictor should be kept in the model. Otherwise, it can be dropped.