. Each observation in the following data set shows a person\'s income (measured

Question

. Each observation in the following data set shows a person's income (measured in thousands of dollars) and whether that person purchased a particular product last year. Assign a zero for a No purchase and a 1 for a Yes, and estimate a logit model for the purchase of this product. Write down the estimated logit model; and calculate the probability of buying the product if income is $40 (i.e., $40,000) and if income is $70 (i.e., $70,000). Calculate and interpret the meaning of the odds ratio if income changes from $70 to $71. What is the value of the concordance index and its meaning? PersonIncome (000) Purchase $31 $50 S33 $77 $54 $78 $21 $46 $66 No No No Yes Yes Yes No Yes No Yes 10 $89

Explanation / Answer

The Logistic Regression Model are,

> Model

Call: glm(formula = Purchase ~ Income)

Coefficients:

(Intercept) Income  

-0.34519 0.01551  

Degrees of Freedom: 9 Total (i.e. Null); 8 Residual

Null Deviance: 2.5

Residual Deviance: 1.391 AIC: 14.65

Fitted Logistic Model from above result :

Purchase = -0.34519 + 0.01551 * Income

The Predicted Values are,

[,1]
[1,] 0.13556013
[2,] 0.43021364
[3,] 0.16657629
[4,] 0.84893179
[5,] 0.49224596
[6,] 0.86443987
[7,] -0.01952066
[8,] 0.36818133
[9,] 0.67834291
[10,] 1.03502874

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