# Regression vs Linear Model

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.

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
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
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(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
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

• What is "general linear regression"? Can you show your model results? – The Laconic Dec 10 '18 at 4:21
• Of course! Edited to show model results. I'm using Minitab if that makes a difference – Ryan Dec 13 '18 at 4:20
• My guess is that shaft diameter varies with material and/or company, which I think is what you’re getting at with your worry about confounding. Do different companies specialize in different geometries? Do geometries depend on the material? Domain knowledge (that I don’t have) would probably suggest an answer. – The Laconic Dec 13 '18 at 4:48
• This cannot be answered without more context. – kjetil b halvorsen Mar 29 '19 at 14:07