Solved – How to compare coefficients within the same multiple regression model

rregressionregression coefficients

As the titles states, I would like to compare two coefficients in my multiple regression model but I'm not quite sure how.

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)       68.9483    29.7439   2.318 0.024493 *  
Shots.PG          -0.5074     1.4696  -0.345 0.731334    
Shots.OT.PG        7.4992     3.1410   2.388 0.020707 *  
Dribbles.PG        0.6081     0.8121   0.749 0.457401    
Fouled.PG         -0.9856     0.8783  -1.122 0.267031    
Offsides.PG        1.0520     3.0728   0.342 0.733477    
Tackles.PG         0.2705     0.6721   0.402 0.689016    
Fouls.PG          -0.4230     0.7893  -0.536 0.594329    
Ints.PG            0.3414     0.5962   0.573 0.569451    
Shots.Allowed.PG  -3.3604     0.8063  -4.167 0.000119 ***

Above are the results I've obtained. At first glance I thought it was interesting Shots OT has double the impact of Shots Allowed but I see that their standard errors are significantly different so that worries me.

How would I go about comparing these two values?

Using linear.hypothesis() I get:

Linear hypothesis test

Hypothesis:
Shots.OT.PG  + 2 Shots.Allowed.PG = 0

Model 1: restricted model
Model 2: Points ~ Shots.PG + Shots.OT.PG + Dribbles.PG + Fouled.PG + Offsides.PG + 
    Tackles.PG + Fouls.PG + Ints.PG + Shots.Allowed.PG

  Res.Df    RSS Df Sum of Sq      F Pr(>F)
1     52 4488.5                           
2     51 4484.2  1    4.2107 0.0479 0.8277

How do I interpret this? Does this mean they are not different due to its large P Value. I am trying to find out whether or not the Shots OT has a larger effect on the Points total than the Shots Allowed PG

Best Answer

Assuming md1 is lm model. You could use linear.hypothesis from car package. Test

linear.hypothesis(md1, "Shots.OT.PG = -2*Shots.Allowed.PG")

If your p-value is greater than 0.05 you could not reject the Null Hypothesis, in this case, in absolute values, Shots.OT.PG coefficient is not different from the double of Shots.Allowed.PG coefficient.

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