I have the following data in Stata with three variables: 1- High school GPA (out of a 100) 2- job search duration in months 3- Sqr root of job search duration in months
dataex HS_gpa log_HS_gpa durationInMonths sqrt_durationInMonths
clear
input float(HS_gpa log_HS_gpa durationInMonths sqrt_durationInMonths)
74.38 4.309187 246 15.684387
70 4.248495 262 16.186415
76 4.3307333 112 10.583005
75 4.317488 190 13.78405
87 4.465908 470 21.679483
I am testing with a bivariate regression the relationship between one's HS GPA and their job search duration, so I ran the regression below:
regress durationInMonths HS_gpa
Source | SS df MS Number of obs = 2,905
-------------+---------------------------------- F(1, 2903) = 12.21
Model | 19.4647825 1 19.4647825 Prob > F = 0.0005
Residual | 4626.0168 2,903 1.59352973 R-squared = 0.0042
-------------+---------------------------------- Adj R-squared = 0.0038
Total | 4645.48158 2,904 1.59968374 Root MSE = 1.2624
durationIn~s | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
HS_gpa | -.0087986 .0025175 -3.49 0.000 -.0137349 -.0038624
_cons | 3.029813 .2167351 13.98 0.000 2.604843 3.454783
However, I thought that the relationship may not be linear so I created square root variable of the "durationInMonths" variable and ran the same regression again. I further created a log variable of highschool GPA.
The direction of the coefficient is the same, but higher at "-.249" for log_HS_gpa.
regress sqrt_durationInMonths log_HS_gpa
Source | SS df MS Number of obs = 2,905
-------------+---------------------------------- F(1, 2903) = 14.24
Model | 2.30839189 1 2.30839189 Prob > F = 0.0002
Residual | 470.701254 2,903 .162143043 R-squared = 0.0049
-------------+---------------------------------- Adj R-squared = 0.0045
Total | 473.009646 2,904 .162882109 Root MSE = .40267
sqrt_durat~s | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
log_HS_gpa | -.2499674 .0662488 -3.77 0.000 -.3798667 -.120068
_cons | 2.564629 .2944605 8.71 0.000 1.987256 3.142001
