Question

When I ran a bivariate regression, I got the following table

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 10.8681 2.8754 3.780 0.000157 ***
ETHWAR -1.0170 0.4524 -2.248 0.024570 *

When I ran a multivariate regression, I got the following table

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 10.811 2.987 3.619 0.000296 ***
ETHWAR -13.804 4844.876 -0.003 0.997727
CIVTOT 12.730 4844.877 0.003 0.997903

Why did the p-value for ETHWAR change? And why did it change so dramatically?

Answer 1

Ans-

As small the p-value (< 0.05 at 5% level of signficance) indicates that you can reject the null hypothesis. In other words, a predictor that has a low p-value is likely to be a meaningful addition to your model because changes in the predictor's value are related to changes in the response variable.

Conversely, a larger (insignificant) p-value suggests that changes in the predictor are not associated with changes in the response.

In the case of bivariate regression , we can see that the predictor variables ETHWAR is 0.024570< 0.05 it means ETHWAR is significant because the p-values<0.05

but in case of multiple regression  we can see that the predictor variables of ETHWAR and CIVTOT are not significant because both of their p-values are greater than 0.05 at alpha level of 0.05, which indicates that it is not statistically significant.

it may be happen because of wrong statistical tool , and it may happen that CIVTOT having more impact on dependent variable.