# Step by step regression

#### pepsico007

##### New Member
I am doing some analysis on relationship between bond spread and the factors (like bond rating, originator information, duration etc.).

I can do a regular linear regression like spread ~ rating + originator + duration, but my friend using the “multiply way”, and I am not sure if there is any theory that support his methodology.

Below is how he do it:
1. He first consider that spread ~ (alpha1 + beta1*rating) * f(originator information, duration); by the historical data he can solve alpha1, beta1, and f(origination information, duration) (treat f as a whole independent variable);
2. Let Y = spread / (alpha1 + beta1*rating), then he has Y ~ (alpha2 + beta2*originator information) * f(duration), again solve alpha2, beta2, and f(duration);
3. Let Y_hat = Y / (alpha2 + beta2*originator information), then he has Y_hat ~ alpha3 + beta3*duration, and solve alpha3, beta3;

He insists that by dividing each factors, he can separate the impact of each factor from spread, like the final Y_hat only have impact of duration, when plot the figure of Y_hat and duration, I do see that Y_hat "log increase" as duration goes up, and he think the result is cool.

My concern is that, even the result looks good, but I am not sure if there is any theory that can support this methodology, because I haven't seen this method before.