# Why the value of Coefficient of variable is different when it used as single variable as compared to multivariable model

#1

I am currently solving one classification problem in which I have created a simple logistic regression model using an only single variable in each coefficient value of the variable is something else then when I have used the variable to make a multivariable model.

mod1=glm(factor(Crop_Damage)~Number_Weeks_Used,family = binomial,data = train_new[,-1])

summary(mod1)

``````Call:
glm(formula = factor(Crop_Damage) ~ Number_Weeks_Used, family = binomial,  data = train_new[, -1])

Deviance Residuals:
Min       1Q   Median       3Q      Max
-1.1218  -0.6293  -0.4962  -0.3982   2.5507

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)       -3.2135890  0.0278877 -115.23   <2e-16 ***
Number_Weeks_Used  **0.0513552**  0.0007927   64.79   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 79458  on 88857  degrees of freedom
Residual deviance: 74993  on 88856  degrees of freedom
AIC: 74997

Number of Fisher Scoring iterations: 4
``````

Using all the variable

``````mod=glm(factor(Crop_Damage)~.,family = binomial,data = train_new[,-1])
summary(mod)

Call:
glm(formula = factor(Crop_Damage) ~ ., family = binomial, data = train_new[,
-1])

Deviance Residuals:
Min       1Q   Median       3Q      Max
-1.6140  -0.6042  -0.4605  -0.3572   2.7729

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)             -4.024e+00  7.966e-02 -50.512  < 2e-16 ***
Estimated_Insects_Count  6.492e-04  1.594e-05  40.732  < 2e-16 ***
Crop_Type               -4.536e-01  2.356e-02 -19.252  < 2e-16 ***
Soil_Type               -1.456e-01  1.970e-02  -7.391 1.46e-13 ***
Pesticide_Use_Category   7.135e-01  2.513e-02  28.395  < 2e-16 ***
Number_Doses_Week       -7.050e-03  7.147e-04  -9.864  < 2e-16 ***
Number_Weeks_Used        1.258e-02  1.162e-03  10.828  < 2e-16 ***
Number_Weeks_Quit       -2.601e-02  1.634e-03 -15.922  < 2e-16 ***
Season                  -5.752e-03  1.357e-02  -0.424    0.672
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 79458  on 88857  degrees of freedom
Residual deviance: 72035  on 88849  degrees of freedom
AIC: 72053
``````

I want to know the reason why this happening

#2

@harry - The value of coefficient of a variable is different when you have used a single variable as comapred to when the variable is used as combination with other variable there is a major reason is the corelation between the variable .
correlation - It tells about the relation between two variable.

Therefore there is differnce between the value of coefficent (Number_Weeks_Used) when it is used as a single variable as compared when it is used with other variables.

Hope this helps!

Regards,
Hinduja