This assignment is based on the module on Logistic Regression.

The outcome variable in this dataset is the variable sold, which labels whether an iPad listed on eBay was sold (equal to 1 if it did, and 0 if it did not). The independent variables consist of 9 pieces of product data available at the time the iPad listing is posted, and a unique identifier.

Here is the data:

• Data: eBay Data
• https://drive.google.com/file/d/1pNG2V_eUSpAw33CM6N-W3qhZUND7Rg0p/view?usp=drivesdk

Question 1(2 points)

Simpler models are generally preferred to more complex models because they are less likely to overfit the data. So, let us drop out non-signficant variables from model1 above but keep variables that previous research or experience indicates should have an effect. So, estimate model2 with the following variables:

biddable, startprice,condition, storage, productline,upperCaseDescription,startprice_99end

What is the AIC?

(If you are surprised by a drop in AIC from model1 to model2, it is because AIC = 2k - 2LL = 2k + (-2LL). Now, -2LL is a measure of error and is similar to SSE (from linear regression). Simpler models such as model2 will always have -2LL that is larger than that for complex models like model1. To address this, AIC applies a penalty with the term 2k (where k is number of parameters or number of coefficients). For model1, 2k is much larger than 2k for model2.)

Question 2(2 points)

Based on the coefficient of upperCaseDescription, what advice would you give someone selling iPads on eBay?

Question 2 options:

	Use a lot of upper case letters in the description
	Use very few upper case letters in the description

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Question 3(2 points)

You will note that the data contains a number of factor variables. In order to model factor variables, they have to be dummy coded. Fortunately, glm and lm functions automatically dummy code factor variables and then run the dummy variables in the model. The first level is usually selected to be the baseline or reference variable to which each of the other levels is compared. Review the results of model2 and the coefficients of the variables. (After controlling for the effects of all other variables in the model), what sells better iPad3 or iPad 1?

(Now for yourself, after answering the above question, see if you can also find out how much better one sells than the other!)

Question 3 options:

	iPad 1
	iPad 3

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Question 4(2 points)

If startprice goes up by $1, what will be the % reduction in the chance of selling an iPad. To interpret coefficients in logistic regression, you have to exponentiate the coefficient. E.g., exp(coefficient)

Question 4 options:

	No change
	1%
	2%
	5%

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Based on model2 (and controlling for the effects of all other variables), how much more (or less) likely is an iPad Air 1/2 to sell compared to an iPad 1?

Question 5 options:

	iPad 1 is 6.6 times (or 560%) more likely to sell than iPad Air 1/2
	iPad 1 is 1.88 times (or 88%) more likely to sell than iPad Air 1/2
	iPad Air 1/2 is 6.6 times (or 560%) more likely to sell than iPad 1
	iPad Air 1/2 is 1.88 times (or 88%) more likely to sell than iPad 1

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Question 6(2 points)

Now, let us run one more model called model_productline. For this model, predict the variable 'sold' using only 'productline'. Is the sign of the coefficient for iPad Air1/2 in this model the same as that in model2?

(Your conclusion may make you feel uncomfortable. The explanation lies in the fact that a multiple logistic regression controls for the effects of all other variables such as startprice but a simple logistic regression does not.)

Question 6 options:

	Yes
	No