# estimation of variance of slope and intercept in logistic regression

let us suppose we have following data

i would like to test whether number of hours of studying helps me to predict student will pass or not, i used following step, initially i give some values to slope and intercept

$\beta_1=0.1$

$\beta_0=0.1$

after that i have calculated $L$ as

$L=\beta_1 \cdot\text{Hours}+\beta_0$

and also i have calculated probabilities , all calculation is shown on screenshot

finally i have calculate sum of last calculated part and i have got

-13.27734511

using solver i have estimated slope and intercepts, also i have calculated estimated probabilities and residuals

Slope       1.510731897
Intercept   -4.346648201

now i have following questions

1. how to calculate std error of intercepts and slope ?
2. how to calculate P value using Wald test ?

please give me hint and i will try to solve myself

• Nothing like Wald tests to make me feel I'm rusty in some things. A Wald test is a linear approximation used when an exact test is computationally expensive. The MLEs for slope and intercept in problems like this are found by iterative numerical methods. I'm guessing that at stats.stackexchange.com some of the regular posters know the answer to this one off the top of their heads. (And there's probably software that does this; I would actually be a bit surprised if it can't be done in R.) $\qquad$ – Michael Hardy Sep 18 '17 at 17:49
• then could you please migrate this question to the stats.stackexchange.com – dato datuashvili Sep 18 '17 at 17:55
• i am doing by excel because i want to calculate by hand and learn – dato datuashvili Sep 18 '17 at 17:56
• I've voted to migrate the question to stats.stackexchange.com . Apparently at least two other such votes are needed. – Michael Hardy Sep 19 '17 at 1:19