Refer to Data Set HORMONE.DAT at www.cengagebrain .com. Use...

Refer to Data Set HORMONE.DAT at www.cengagebrain .com.
Use logistic-regression methods to assess whether presence of biliary secretions during the second period (any or none) is related to the type of hormone used during the second period.

Key Concepts

Logistic Regression

Logistic regression is a statistical method used to model the relationship between a binary dependent variable and one or more independent variables. It estimates the probability that an event occurs by fitting data to a logistic function, and is widely used in cases where the outcome is categorical, such as yes/no or presence/absence of a characteristic.

Binary Outcome Variable

A binary outcome variable is one that takes on one of two possible values, such as success/failure or presence/absence. In logistic regression, this variable is modeled to estimate the probability of one outcome over the other, and is central to the proper formulation and interpretation of the model.

Categorical Predictor Variable

A categorical predictor variable is one that represents distinct groups or categories without any inherent numerical ordering. In logistic regression, these variables are often included as dummy variables to compare the effect of different categories on the likelihood of the binary outcome, allowing researchers to assess the differences between groups.

Odds Ratio Interpretation

An odds ratio in logistic regression is a measure of association that quantifies how the odds of the outcome change with a one-unit change in the predictor variable, or between different categories of a categorical predictor. It provides a meaningful way to interpret the effect size in terms of the likelihood of the event occurring in response to changes in the predictors.

Transcript

00:02 Okay, so what we have here is an equation that defines the rate of change of the level of hormone in the blood on a 24 -hour cycle.

00:09 So we are given with the values of lambda, which is equal to beta, is equal to 1, k is equal to 2, and x not is equal to 10.

00:19 So we are required to get for the value of x of t.

00:26 So what we're going to do first is to substitute the given values to the equation.

00:36 So by doing so, we now have dx over dt is equal to 1 minus cosine of phi t over 12 minus 2x.

00:53 So rearranging the equation, we have dx over dt plus 2x is equal to 1 minus cosine of phi t over 12.

01:08 And as you can see, this is now a linear differential equation, wherein the dependent variable is x and the independent variable is t.

01:20 So now we want to find the integrating factor.

01:23 So our p of t is equal to 2 and solving for the integrating factor of mu of t is equal to e raise to the integral of 2dt is equal to e raise to 2t.

01:39 So this is now our integrating factor.

01:42 So multiplying both sides by the integrating factor, we have e raise to 2t, dx over dt plus 2x, erase to 2t is equal to e raise to 2t times 1 minus cosine of pi t over 12, which is also equal to e raise to 2t times 1 minus cosine of pi t over 12, which is also equal to e raise to 2t minus e raise to 2t cosine p of t over 12.

02:24 So we know that we can express the left side of the equation as d over dt e raise to 2t x is equal to e raise to 2t minus e raise to 2t cosine of pi t over 12.

02:50 So taking the integral of both sides, we have x, x, e raise to 2t on the left side, and one half, e raise to 2t minus the integral of e raise to 2t, cosine of pi t over 12 dt.

03:11 So this is a complex one, so you can solve this by doing double...

Please give Ace some feedback