Suppose that we are working with some doctors on heart attack patients. The dependent variable is whether the patient has had a second heart attack within 1 year (yes-1). We have two independent variables, one is age of the patient and the other is a score on anxiety scale (a higher score means more anxious). After applying logistic regression model, we have the following output: Deviance Residuals: Min 10 Median -1.064 30 0.000 Маx 0.000 0.000 1.446 Coefficients: (Intercept) Age Anxiety Estimate Std. Error z value Pr (>|z|) 0.998 0.998 -471.441 223186.509 -0.002 6.394 3057.349 0.002 1.347 611.470 0.002 0.998 (Dispersion parameter for binomial family taken to be 1) Null deviance: 27.7259 on 19 degrees of freedom Residual deviance: 3.7087 on 17 degrees of freedom AIC: 9.7087 Number of Fisher Scoring iterations: 23 a. Determine the estimated logistic regression equation. b. Calculate the odds ratio and interpret.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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![Suppose that we are working with some doctors on heart attack patients. The dependent
variable is whether the patient has had a second heart attack within 1 year (yes=1). We have
two independent variables, one is age of the patient and the other is a score on anxiety scale (a
higher score means more anxious). After applying logistic regression model, we have the
following output:
Deviance Residuals:
10 Median
Min
30
Маx
|-1.064
0.000
0.000
0.000
1.446
Coefficients:
Estimate Std. Error z value Pr (>Iz])
(Intercept)
Age
-471.441 223186.509
-0.002
0.998
6.394
3057.349
0.002
0.998
Anxiety
1.347
611.470
0.002
0.998
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 27.7259 on 19 degrees of freedom
Residual deviance: 3.7087 on 17 degrees of freedom
AIC: 9.7087
Number of Fisher Scoring iterations: 23
a. Determine the estimated logistic regression equation.
b. Calculate the odds ratio and interpret.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff725c8e5-fe0a-4dea-8448-a47cd0efbca7%2Fe52c6309-9e19-425f-983d-de87991ea0a1%2Fe6if7fi_processed.jpeg&w=3840&q=75)
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