10 2.3 Exercises

The following exercises ask questions about a dataset of 291 apartments sold in Daegu, South Korea in recent years.

A few rows of the dataset are shown here:

SalePrice	YrSold	Size(sqf)	Floor	TimeToSubway	SubwayStation
159292	2012	914	8	10min~15min	Kyungbuk_uni_hospital
60176	2011	587	7	5min~10min	Daegu
79646	2009	644	9	15min~20min	Myung-duk
185840	2014	914	22	15min~20min	Myung-duk
194690	2013	903	7	0-5min	Myung-duk

10.1 Exercises 2.3.1

The following is a map of the Daegu subway system:

There are three major downtown stations: Cheong-Na Hill (does not appear in this dataset), Banwoldang, and Myeongdeok (Myong-duk).

We first like to know whether the regions near the two major stations are similarly priced. The table below gives some summary statistics:

SubwayStation	mean_price	sd_price	count
Bangoge	169583.6	65069.48	36
Banwoldang	312262.1	100677.98	37
Chil-sung-market	114690.0	54548.18	5
Daegu	132189.5	105165.58	4
Kyungbuk_uni_hospital	256527.8	102699.74	82
Myung-duk	158532.9	83788.47	75
Sin-nam	260563.6	92617.54	32
no_subway_nearby	228331.4	101290.71	20

Do Myung-duk and Banwoldang regions have similarly priced apartments?

Compute the relevant summary statistic to answer the question.
Compute the standard deviation of the summary statistic.
Report and interpret a standardized score.

10.2 Exercises 2.3.2

Perhaps apartments are more expensive in the Banwoldang area because they tend to be closer to the subway station.

The following table gives summary statistics for the variable SubwayStation, which tells the nearest station to the apartment; and the variable TimeToSubway, which tells long it takes to ride the bus to the nearest subway station.

SubwayStation	0-5min	10min~15min	15min~20min	5min~10min	no_bus_stop_nearby
Bangoge	0	0	0	36	0
Banwoldang	33	0	0	4	0
Chil-sung-market	0	0	5	0	0
Daegu	0	0	0	4	0
Kyungbuk_uni_hospital	56	26	0	0	0
Myung-duk	17	13	45	0	0
no_subway_nearby	0	0	0	7	13
Sin-nam	29	0	0	3	0

We are interested in answering the research question: Is an apartment near Banwoldang more likely to be a <5 minute commute than an apartment near Myung-duk?

Compute the relevant summary statistic to answer the question.
Compute the standard deviation of the summary statistic.
Report and interpret a standardized score.

10.3 Exercises 2.3.3

Perhaps region (or proximity to subway station) is not the only thing that impacts the price of the apartments.

The following table shows the correlations between the quantitative variables in this dataset:

Variable	SalePrice	Size.sqf.	Floor
SalePrice	1.0000000	0.7402109	0.3658820
Size(sqf)	0.7402109	1.0000000	0.1986749
Floor	0.3658820	0.1986749	1.0000000

Notice that the correlations between every variable and itself is 1. Why is this?
Is there evidence of a relationship between price of an apartment and size?
Is there evidence of a relationship between price of an apartment and which floor it is on?
Suppose we converted the TimeToSubway variable into a quantitative variable, representing each range by it’s midpoint. (For example, the category 5min-10min would become the number 5.5.) Do you think the correlation between this variable and the Sale Price would be positive, negative, or approximately zero? Why?