Attempting to interpret both Beta Regression and transformed DV model results

After reading a good amount of the answered questions on interpreting Beta Regression results (Best explanation here) and reading through the Betareg vignette, I still feel a lack of confidence writing my interpretations into my thesis. Just a bit of background first: I ran the following code, which by default uses a logit link:

betaMod <- betareg(BEVMarketShare ~ CumulFastStations + CumulNormalStations +
IncentAvail + ModelsAvail + Price + Range + TechRatio +
FuelPrices , data= OutliersRemoved)


Here's a small sample of my data:

Here are the results:

Let's take CumulFastStations for example, where the coefficient is 0.004756. If I use the interpretation I've come to understand best, for every additional Fast Charging Station added in a Bundesland you would expect relative change in the BEV Market Share by 4% in E(BEVMarketShare) / (1−E(BEVMarketShare)). So whether or not this is correct, I feel a bit strange repeating this for the various regressors I'd like to make predictions for. I've seen that it's also possible to use the predict function, but I'm having trouble figuring out why this code results in the error "Error in eval(predvars, data, env) : object 'CumulNormalStations' not found":

Test <- data.frame(CumulFastStations = seq(0, 300, by = 25))
Test\$BEVMarketShare <- predict(betaMod, newdata = Test)
print(Test)
plot(BEVMarketShare ~ CumulFastStations, data = Test, type = "b")


My other question is possibly nonsense. I preformed regression on the same model above, however with the DV BEVMarketshare logit transformed:

logitvar_model <- lm(logit(BEVMarketShare) ~ CumulFastStations +
CumulNormalStations + ModelsAvail + Range + TechRatio +
FuelPrices, data = OutliersRemoved)


I'm only doing this to try to replicate the method used by one relevant study to my topic. The screenshot of the where the author notes his method seems to clearly indicate he performed a logit transformation on the DV.

So now I'm again confused on how to interpret the coefficients. I've only found information on logit regression, but not for a transformation with logit on the DV such as this .

I hope this isn't too much to digest, but I'm really kind of stuck with these two issues. Thank you very much in advance!

• I've only found the following material regarding the interpretation of logit transformed DVs in the "Beta Regression in R" introduction paragraph: "The usual practice used to be to transform the data so that the transformed response, say ˜y, assumes values in the real line and then apply a standard linear regression analysis. A commonly used transformation is the logit, ˜y = log(y/(1−y)). This approach, nonetheless, has shortcomings. First, the regression parameters are interpretable in terms of the mean of ˜y, and not in terms of the mean of y (given Jensen’s inequality)." – Pazappa the napper Jul 12 '18 at 19:25

I've looked into predicting for the Beta regression model and have found the following solution:

newdata <- data.frame("CumulFastStations"=c(30,31,32,33),
"CumulNormalStations"=342.69, "IncentAvail"=1,  "ModelsAvail"=38,
"Price"=38532.41, "Range"=278.48,
"TechRatio"=8.79,
"FuelPrices"=1.3403)

predict(betaMod,newdata)


First I took the averages from my very last period (not shown, but the values are inserted in the code above) and created a new data frame. For predicting 'CumulFastStations' I just added increments of one to the average, holding everything else constant, and got:

 1           2           3           4
0.008577655 0.008618191 0.008658918 0.008699835


I'm still unsure of interpretation for the logit transformation model, but hopefully someone else can answer this.