# How to interpret Dickey-Fuller Results

I want to prove that my data is non-stationary at level, but stationary after first differencing. I am trying to do this with the ur.df() function in R, but I am a little confused about the results

Since the goal is to do multiple linear regression with several independent variables (and no lags), I did lag = 0

summary(ur.df(stresstest$U.S._Mortgage_rate_Base, lag = 0)) ############################################### # Augmented Dickey-Fuller Test Unit Root Test # ############################################### Test regression none Call: lm(formula = z.diff ~ z.lag.1 - 1) Residuals: Min 1Q Median 3Q Max -0.73167 -0.22969 0.06761 0.17445 0.76329 Coefficients: Estimate Std. Error t value Pr(>|t|) z.lag.1 0.007198 0.008796 0.818 0.417 Residual standard error: 0.279 on 47 degrees of freedom Multiple R-squared: 0.01405, Adjusted R-squared: -0.006932 F-statistic: 0.6696 on 1 and 47 DF, p-value: 0.4173 Value of test-statistic is: 0.8183 Critical values for test statistics: 1pct 5pct 10pct tau1 -2.62 -1.95 -1.61  Do I need to look at the p-value here, or the test statistic? I interpreted this as the data has a unit root, because the p-value is greater than 0.05. I then redid the analysis with the first differences: summary(ur.df(diff(stresstest$U.S._Mortgage_rate_Base), lag = 0))


In this case, the p-value was less than 0.05 so the data is stationary. Therefore, the data is I(1) stationary

Is this a correct interpretation?