# Solved – Looking for a layman’s explanation of how to manually calculate log odds

I will start that I am not as math oriented as I would like to and could use a layman's / non-staticians explanation walk through of how to calculate the log odds.

I am reading Hosmer, Lemeshow, and Sturdivant's Appliged Logistical Regression which is helpful, but I could use a primer / tutorial to help solidify the concepts for me.

Given something like the following equation (values randomly chosen):
\$\$
logbigg(frac pi {(1-pi)}bigg) = 0.3211 + 0.27 X_1 + 0.732 X_2
\$\$
And the following information:

• Indicator Variable Group A \$X_2 = 1\$, Group B \$X_2 = 0\$.
• Sample Size 1000
• Likelihood Value for Model = 0.0598

How would I compute the following from the above information manually without using R or another application.

1. Log Odds for \$X_1 = 3\$ for each group.
2. Odds for \$X_1 = 3\$ for each group.
3. Probability \$X_1 = 3\$ for each group.

If I understand correctly the Log Odds is the \$ln(p/(1-p))\$ and log-odds and odds are different; but I am NOT clear on how to apply the above information to calculate the above information and am looking for a step-by-step walk through that covers most of the steps required of how to apply this information and perform the calculation.

Note: While I am utilizing this to assist me in a class it is not part of an assignment or test and the equation is made up by me purely for example purposes as I feel I am in need of a starting point example as I've spent some time reading the book (particularly chapter 3) but it is not clicking like I need it to.

Contents

begin{align} text{odds}(X_1 = 3; A) &= e^{1.8631} \ &= 6.443681 \ \ text{odds}(X_1 = 3; B) &= e^{1.1311} \ &= 3.099064 end{align} (Full disclosure: I used `R` to do the arithmetic on that one.)
begin{align} text{probability}(X_1 = 3; A) &= frac{6.443681}{6.443681 + 1} \ \ &= 0.8656579 \ \ text{probability}(X_1 = 3; B) &= frac{3.099064}{3.099064 + 1} \ \ &= 0.7560419 end{align} (I used `R` for this one, too.)