@aquev Hi thanks for your interest in sparklyr! 
For question 1, you can print the standard error of the coefficients and the intercept with the following:
library(sparklyr)
spark_version <- "2.4.4" # This is the version of Spark I ran this example code with,
# but I think everything that follows should work in all versions of Spark anyways
sc <- spark_connect(master = "local", version = spark_version)
cached_cars <- copy_to(sc, mtcars)
model <- cached_cars %>%
ml_linear_regression(mpg ~ .)
coeff_std_errs <- invoke(model$model$.jobj, "summary") %>%
invoke("coefficientStandardErrors") %>%
print(coeff_std_errs)
We probably should make those numbers part of the summary output in R.
I'm not sure if I understood what question 2 and question 3 meant exactly. Please elaborate, with a small example, or a link to relevant maths formula, if possible. I'll be more than happy to see what can be done in sparklyr to address those use cases.