Each observation in the following data set shows a person\'s income (measured in
ID: 3063327 • Letter: E
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?
Person
Income (000)
Purchase
1
$31
No
2
$50
No
3
$33
No
4
$77
Yes
5
$54
Yes
6
$78
Yes
7
$21
No
8
$46
Yes
9
$66
No
10
$89
Yes
Person
Income (000)
Purchase
1
$31
No
2
$50
No
3
$33
No
4
$77
Yes
5
$54
Yes
6
$78
Yes
7
$21
No
8
$46
Yes
9
$66
No
10
$89
Yes
Explanation / Answer
With the given data, the logistic model is
Purchase = exp(-4.98858 + (0.09213*Income))/(1 + exp(-4.98858 + (0.09213*Income)))
When the income is 40,000, the estimated probability is 0.2136 and when income is 70,000 the estimate probability is 0.8116
The odds ratio when income changes from 70 to 71 is 1.01686 which means that you are 1.01686 times more likely to purchase when your income is 71000 than when your income is 70000
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