We will begin our discussion of binomial logistic regression by comparing it to regular ordinary least squares (OLS) regression. Perhaps the most obvious difference between the two is that in OLS regression the dependent variable is continuous and in binomial logistic regression, it isbinary and coded as 0 and 1. Because the dependent variable is binary, different assumptions are made in logistic regression than are made in OLS regression, and we will discuss these assumptions later. Logistic regression is similar to OLS regression in thatit is used to determine which predictor variables are statistically significant, diagnostics are used to checkthat the assumptions are valid, a test-statistic is calculated that indicates ifthe overall model is statistically significant, and a coefficient and standarderror for each of the predictor variables is calculated.To illustrate the difference between OLS and logistic regression, let’s see what happens when data with a binary outcome variable is analyzed using OLS regression.

1. Logistic Regression In Excel

For the examples in this chapter, we will use a set of data collected by the state of California from 1200 high schoolsmeasuring academic achievement. Our dependent variable is called hiqual.This variable was created from a continuous variable ( api00) using a cut-off point of745. Hence, values of 744 and below were coded as 0 (with a label of 'nothighqual')and values of 745 and above were coded as 1 (with a label of 'highqual'). Our predictor variable will be a continuous variable called avged, which is acontinuous measure of the average education(ranging from 1 to 5) of the parents of the students in the participating high schools. After running the regression, we will obtain the fitted values and then graph themagainst observed variables.NOTE: You will notice that although there are 1200 observations in thedata set, only 1158 of them are used in the analysis below. Cases withmissing values on any variable used in the analysis have been dropped (listwisedeletion).

We will discuss this issue further later on in the chapter. Use clearregress hiqual avgedSource SS df MS Number of obs = 1158-+- F( 1, 1156) = 1136.02Model 126.023363 1 126.023363 Prob F = 0.0000Residual 128.2.110934276 R-squared = 0.4956-+- Adj R-squared = 0.4952Total 254.2.219760921 Root MSE =.33307-hiqual Coef. T P t 95% Conf. Interval-+-avged.4286426.0127175 33.70 0.000.4036906.4535946cons.8549049.0363655 -23.51 0.000.9262547.7835551-predict yhat(option xb assumed; fitted values)(42 missing values generated)twoway scatter yhat hiqual avged, connect(l.) symbol(i O) sort ylabel(0 1)In the graph above, we have plotted the predicted values (called 'fittedvalues' in the legend, the blue line) along with the observed data values (thered dots). Upon inspecting the graph, you will notice that some things that do not make sense. First, there are predicted values that are less than zero and others that are greater than+1. Such values are not possible with our outcome variable.

Also, the line does a poor job of'fitting' or 'describing' the data points. Now let’s try running the same analysis with a logistic regression. Logit hiqual avgedIteration 0: log likelihood = -730.68708Iteration 1: log likelihood = -414.55532Iteration 2: log likelihood = -364.17926Iteration 3: log likelihood = -354.51979Iteration 4: log likelihood = -353.92042Iteration 5: log likelihood = -353.91719Logistic regression Number of obs = 1158LR chi2(1) = 753.54Prob chi2 = 0.0000Log likelihood = -353.91719 Pseudo R2 = 0.5156-hiqual Coef. Z P z 95% Conf.

Interval-+-avged 3.909635.2383083 16.41 0.000 3.442559 4.376711cons -12.30054.7314646 -16.82 0.000 -13.73418 -10.86689-predict yhat1(option p assumed; Pr(hiqual))(42 missing values generated)twoway scatter yhat1 hiqual avged, connect(l i) msymbol(i O) sort ylabel(0 1)As before, we have calculated the predicted probabilities and have graphedthem against the observed values. With the logistic regression, we getpredicted probabilities that make sense: no predicted probabilities isless than zero or greater than one. Also, the logistic regression curvedoes a much better job of 'fitting' or 'describing' the data points. TerminologyNow that we have seen an example of a logistic regression analysis, let’s spend a little time discussing the vocabularyinvolved. So let’s begin by defining the various terms that are frequently encountered, discuss how these terms are related to one another and how they are used to explain the results of the logistic regression.Probability is defined as the quantitative expression of the chance that an event will occur.

Logistic Regression In Excel

More formally, it is the number of times the event'occurs' divided by the number of times the event 'could occur'. For a simple example, let’s consider tossing a coin. On average, you get heads once out of every two tosses. Hence, the probability of getting heads is 1/2 or.5.Next let’s consider the odds. In common parlance, probability and odds are usedinterchangeably. However, in statistics, probability and odds are not the same.

Theodds of an event happening is defined as the probability that the eventoccurs divided by the probability that the event does not occur. To continuewith our coin-tossing example, the probability of getting heads is.5 and theprobability of not getting heads (i.e., getting tails) is also.5.

Hence, the odds are.5/.5 = 1.Note that the probability of an event happening and its compliment, theprobability of the event not happening, must sum to 1. Now let’s pretend that we alter the coin so that the probability of getting heads is.6. The probability of not getting heads is then.4.

The odds of getting heads is.6/.4 = 1.5. If we had altered the coin so that the probability of getting heads was.8, then the odds of getting heads would have been.8/.2 = 4.

As you can see, when the odds equal one, the probability of the event happeningis equal to the probability of the event not happening. When the odds are greater than one, the probability of the event happeningis higher than the probability of the event not happening, and when the odds are less than one, the probability of the event happening is less than the probability of the event not happening. Also note that odds can be converted back into a probability: probability = odds / (1+odds).Now let’s consider an odds ratio. As the name suggests, it is theratio of two odds. Let’s say we have males and females who want to join ateam.

Let’s say that 75% of the women and 60% of men make the team.So the odds for women are.75/.25 = 3, and for men the odds are.6/.4 = 1.5.The odds ratio would be 3/1.5 = 2, meaning that the odds are 2 to 1 that a womanwill make the team compared to men.Another term that needs some explaining is log odds, also known as logit. Log odds are the natural logarithm of the odds.

The coefficientsin the output of the logistic regression are given in units of log odds. Therefore, the coefficients indicate the amount of change expected in the log odds when there is a one unit change in the predictor variable with all of the othervariables in the model held constant. In a while we will explain why the coefficients are given in log odds.

I am working on Sales data. I have binary variable win/loss the opportunities and rest are the activities done by sales force (sales guys) with 40+ variables (different types of activities done for the Opportunity)I build the logistic model on the available data-set, and i found huge VIF value for different Xi's, then i perform stepwise variable reduction procedure for getting less variable in my model. At the end of this process i got 15 indep variable with dependent variableAgain i build same model on new data-set and again i m getting high VIF around(5610,3374.0.561737,2.512324,9.922235. Etc.) for each variableIf u will look at the pairs graph and coefficient result please refer attached picPlease suggest me what should I do further and how to come with my actual model with less error?I am really stuck for further conclusion.