13.19 (a) Generate a correlation matrix for your predictors. Round the results to three decimal places. (b) Based on the correlation matrix, is collinearity a problem? What rules of thumb (if any) are you using?
Correlation Matrix
F O E A F
Floor 1.000 Offices .823 1.000
Entrance .567 .444 1.000
Age -.189 -.241 .136 1.000 Freeway -.331 -.368 -.082 .175 1.000
32sample size
± .349 critical value .05 (two-tail ± .449 critical value .01 (two-tail)
This the information from the crital table if someone could please help me with this I would really appreciate.
Stands For:
F- Floor
O-Office
E-Entrance
A-Age
F-Freeway
To generate a correlation matrix for your predictors, you need to calculate the correlation coefficients between all pairs of variables. Since you already have the correlation coefficients provided in your question, let's construct the correlation matrix using the given information:
Correlation Matrix:
```
Floor Offices Entrance Age Freeway
-------------------------------------------------
Floor 1.000 0.823 0.567 -0.189 -0.331
Offices 0.823 1.000 0.444 -0.241 -0.368
Entrance 0.567 0.444 1.000 0.136 -0.082
Age -0.189 -0.241 0.136 1.000 0.175
Freeway -0.331 -0.368 -0.082 0.175 1.000
```
Note that the correlation coefficient between a variable and itself is always 1.000 (represented diagonally in the matrix).
Now, to determine if collinearity is a problem, we can use some rules of thumb based on the correlation coefficients:
1. Generally, correlation coefficients between -0.1 and 0.1 are considered negligible or very weak.
2. Correlation coefficients between 0.1 and 0.3 or -0.1 and -0.3 are considered weak.
3. Correlation coefficients between 0.3 and 0.6 or -0.3 and -0.6 are considered moderate.
4. Correlation coefficients above 0.6 or below -0.6 are considered strong.
In this case, based on the correlation matrix, we can see that the correlation coefficients between the predictors are mostly moderate or weak. The highest correlation coefficient is 0.823, which indicates a moderate positive relationship between the variables "Floor" and "Offices."
Therefore, based on these rules of thumb, it seems that collinearity is not a significant problem in this scenario. However, further analysis and consideration of the specific context and purpose of the study is always recommended.