I am mechanically testing devices from multiple companies that have slightly different geometry. I want to know whether the geometry plays a role in the results (or if just the company and material drive the difference).
Linear regression shows variable X with correlation (p=0.3); general linear regression shows variable X as having no effect on the model (p>0.4). What is going on?
I am assuming that the more simple linear regression model is being confounded by the lack of predictors and outputting inaccurate results. Is this correct?
Is the lack of significance in a regression model enough to confidently say that variable x is (likely) not influencing results?
If this is a silly basic question, I apologize.
Thanks in advance.
General Linear Model (ANOVA Based)
Material is nested in Company for this model
Backward Elimination of Terms (alpha to remove = 0.1)
Candidate terms: Shaft Diameter, Thread Diameter, Company, Material(Company)
----Step 1--- ----Step 2--- -----Step 3----
Coef P Coef P Coef P
Constant 116 3758 843.5
Shaft Diameter -948 0.401 -993 0.377
Thread Diameter 1036 0.482
Company -526 0.038 -617 0.000 -476.7 0.000
Material(Company) 242 0.175 472 0.079 284.8 0.000
Analysis of Variance
Source DF Seq SS Contribution Adj SS Adj MS F-Value
Company 2 7247546 56.04% 7059609 3529805 71.65
Material 2 2630442 20.34% 2630442 1315221 26.70
Error 62 3054346 23.62% 3054346 49264
Lack-of-Fit 46 2356103 18.22% 2356103 51220 1.17
Pure Error 16 698243 5.40% 698243 43640
Total 66 12932334100.00%
Source P-Value
Company 0.0000000000000001
Material(Company) 0.0000000043283494
Error
Lack-of-Fit 0.3763855668940961
Pure Error
Total
S 223.241 222.326 221.954
R-sq 76.88% 76.69% 76.38%
R-sq(adj) 74.57% 74.77% 74.86%
R-sq(pred) 70.64% 70.95% 71.40%
Mallows’ Cp 7.00 5.50 4.29
α to remove = 0.1
Linear Regression
Regression Analysis: Maximum Force (N) versus Shaft Diameter
The regression equation is
Maximum Force (N) = - 5370 + 2091 Shaft Diameter
Model Summary
S R-sq R-sq(adj)
273.027 62.53% 61.96%
Analysis of Variance
Source DF SS MS F P
Regression 1 8086979 8086979 108.49 0.0000000000000017
Error 65 4845355 74544
Total 66 12932334
Fitted Line: Maximum Force (N) versus Shaft Diameter