Introduction

This is for you if you are looking for interpretation of p-value,coefficient estimates,odds ratio,logit score and how to find the final probability from logit score in logistic regression in R.

Let’s begin !!

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Importing libraries,Reading Data & Looking at Data

Importing the required libraries.MASS is used for importing birthwt dataset

library(MASS) #### Storing the data set named "birthwt" into DataFrame DataFrame <- birthwt #### To read about the dataset use following command by uncommenting #### help("birthwt") #### Check first 3 rows head(DataFrame,3)









## low age lwt race smoke ptl ht ui ftv bwt ## 85 0 19 182 2 0 0 0 1 0 2523 ## 86 0 33 155 3 0 0 0 0 3 2551 ## 87 0 20 105 1 1 0 0 0 1 2557

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Model fitting & Model Summary

Now we will fit the logistic regression model using only two continuous variables as independent variables i.e age and lwt.

#### Fitting the model LogisticModel<- glm(low ~ age+lwt, data = DataFrame,family=binomial (link="logit")) #### Let's check the summary of the model summary(LogisticModel)

## ## Call: ## glm(formula = low ~ age + lwt, family = binomial(link = "logit"), ## data = DataFrame) ## ## Deviance Residuals: ## Min 1Q Median 3Q Max ## -1.1352 -0.9088 -0.7480 1.3392 2.0595 ## ## Coefficients: ## Estimate Std. Error z value Pr(>|z|) ## (Intercept) 1.748773 0.997097 1.754 0.0795 . ## age -0.039788 0.032287 -1.232 0.2178 ## lwt -0.012775 0.006211 -2.057 0.0397 * ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## (Dispersion parameter for binomial family taken to be 1) ## ## Null deviance: 234.67 on 188 degrees of freedom ## Residual deviance: 227.12 on 186 degrees of freedom ## AIC: 233.12 ## ## Number of Fisher Scoring iterations: 4

Basic Maths of Logistic Regression

We must know odds-ratio and logit score in order to understand logistic regression.

What is Odds Ratio

It represents the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure.

Formula for Odds ratio

The mathematical formula for odds ratio is given by:

Odds=probability of success(p)/ probability of failure

=probability of (target variable=1)/probability of (target variable=0)

=p/(1-p)

Formula for logit

The logit score can defined as follows:

logit(p) = log(p/(1-p)) = b0 + b1*x1 + … + bk*xk

Probability Calculation

Let’s follow the steps as below to find the probability of getting “low=1” (i.e probability of getting success).

NOTE: Do not confuse p-value with probability.They are different things

Intercept Coefficients interpretation (b0, b1 and b2)

1. Intercept Coefficient(b0)=1.748773

2. lwt coefficient(b1) =-0.012775

Interpretation: The increase in logit score per unit increase in weight(lwt)

is -0.012775

age coefficient(b2) =-0.039788









Interpretation: The increase in logit score per unit increase in age

is -0.039788

p-value interpretation

3. p-value for lwt variable=0.0397

Interpretation: According to z-test,p-value is 0.0397 which is comparatively low

which implies its unlikely that there is “no relation” between lwt and target variable i.e low.Star next to p-value in the summary shows that lwt is significant variable in predicting low variable.









4. p-value for age=0.2178

Interpretation: According to z-test,p-value is 0.2178 which is comparatively high which implies its unlikely that there is “any relation” between age and target variable i.e low.

Logit score Calculation

5. Let’s consider a random person with age =25 and lwt=55.Now let’s find the logit score for this person

b0 + b1*x1 + b2*x2= 1.748773-0.039788*25-0.012775*55=0.05144(approx).

6. So logit score for this observation=0.05144

Odds ratio calculation

7. Now let’s find the probability that birthwt <2.5 kg(i.e low=1).See the help page on birthwt data set (type ?birthwt in the console)

8. Odds value=exp(0.05144) =1.052786

Probability Calculation

9. probability(p) = odds value / odds value + 1

p=1.052786/2.052786=0.513(approx.)

p=0.513

Interpretation

0.513 or 51.3% is the probability of birth weight less than 2.5 kg when the mother age =25 and mother’s weight(in pounds)=55

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