How to interpret the result of regression hypothesis testing

Can some1 please help me in clearing the following doubt in interpreting the hypothesis testing result.

When we test whether Dividend payout ratio has significant effect on dependent variable. we formulated Ho = 0 v/s Ha not equal to 0

by testing we found that we are rejecting the null hypothesis, and we concluded that payout ratio is significantly different from 0. what does this mean ? different from 0 ?

Doubt 2: same question above but now hypothesized value was given as 0.2 , and now by conducting this test we failed to reject Ho, why the result differ I mean what is the intuition, and also what is the interpretation here that the Payout ratio is not statistically significantly different from 0.2 ??

It means that in our regression model, the slope coefficient on the dividend payout ratio is likely not zero; that means that when the payout ratio changes, we expect the dependent variable to change.

Bob told us that he thinks that the slope coefficient on the dividend payout ratio is 0.2, and we think that Bob’s an idiot. So we tested the hypothesis, and found out that, incredibly, Bob might just have been right this time. Who’da thunk it?

Thanks :slight_smile:

Also can you tell me, when do we use log-log regression model, when say we are given the x1 and x2 values to find Y, when do we take log of those numbers and plug in the regeression equation, and when do we directly plug the given numbers?

If you think that the relationship between y and x is linear (y = _b_0 + b_1_x), you use y and x as is.

If you think that the relationship between y and x is exponential (y = ke^(b_1_x)), you use log(y), but keep x as is.

If you think that the relationship between y and x is a power function (y = kx^(_b_1)), you use log(y) and log(x).

Can you help me out with related examples?

One of the curriculum example was when x1 which number of market maker is 5 and x2 where market capitilazation is given as 100million, we used log of both.

But i am still confused when to make this decision ?

They’ll tell you.

You aren’t expected to make that decision.