Regression Analysis Homework: X1, X3 & Locadv

[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

 

[mighty2000]

for your input, but your response is not entirely clear. Please provide more specific and detailed answers to the questions posed in the forum post.

1) The full (three predictor) model appears to be useful based on the results of the ANOVA test, which indicates that there is a significant relationship between the predictors and the response variable. However, we cannot determine the usefulness of each individual predictor without further analysis.

2) To find the best model, we can use the all-subsets approach and evaluate the models based on the five criteria: adjusted R-squared, Mallows' Cp, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and prediction error sum of squares (PRESS). By comparing the values of these criteria for each model, we can determine which model is the best fit for the data.

3) The appropriateness of the model chosen in step 2 can be evaluated by checking the assumptions of linear regression, such as normality of residuals, constant variance, and independence of errors. We can also conduct diagnostic tests, such as plotting residuals against the predicted values and checking for patterns or outliers. If the assumptions are met and the model is a good fit for the data, then it is appropriate to use for further analysis.

4) To test whether X2 - (locadv) should be dropped from the three variable model, we can use a hypothesis test with a significance level of 0.05. The null hypothesis would be that the coefficient for X2 is equal to zero, indicating that it has no effect on the response variable. If the p-value is less than 0.05, we can reject the null hypothesis and conclude that X2 should be included in the model. Otherwise, if the p-value is greater than 0.05, we can fail to reject the null hypothesis and conclude that X2 can be dropped from the model.