STATISTICKÁ ANALÝZA DATDaniel Svozil

Laboratoř informatiky a chemie, FCHT

Vojtěch Spiwok, ÚBM, FPBT

Informace• přednášky – základy, opáčko, cvičení – R• http://ich.vscht.cz/~svozil/teaching.html• Další literatura

• D. J. Rumsey, Statistics for Dummies, 2011• D. J. Rumsey, Intermediate Statistics for Dummies, 2007

• zápočet, zkouška – bude oznámeno

Valuing houses

SIZE [ft2] COST [$]1 400 112 0002 400 192 0001 800 144 0001 900 152 0001 300 104 0001 100 88 000

How much money should you expect to pay for 1 300 ft2 house?

104 000 $

Same question now with 1 800 ft2 ?

144 000 $

Valuing houses

SIZE [ft2] COST [$]1 400 112 0002 400 192 0001 800 144 0001 900 152 0001 300 104 0001 100 88 000

How much money should you expect to pay for 2 100 ft2 house?

168 000 $21 is just a half between 18 and 24.

What a statistician does?

a) Look at data

b) Program computers

c) Run statistics software

d) Drink beer

Linear relationship

SIZE [ft2] COST [$]1 400 98 0002 400 168 0001 800 126 0001 900 133 0001 400 91 0001 100 77 000

Is there a fixed amount per square foot?

No

What if I change 1 400 to 1 300? What is the answer now?

Yes

Scatter plots (bodový graf)• Please, take a pen and a

paper and draw a scatter plot of these data.

SIZE [ft2] COST [$]

1 400 98 000

2 400 168 000

1 800 126 000

1 900 133 000

1 300 91 000

1 100 77 000

SIZE

PR

ICE

Scatter plots

SIZE [ft2] COST [$]

1 700 53 000

2 100 65 000

1 900 59 000

1 300 41 000

1 600 50 000

2 200 68 000

Is there a fixed price per square foot?

No

Scatter plots

SIZE [ft2] COST [$] $/ft2

1 700 53 000 31.1765

2 100 65 000 30.9524

1 900 59 000 31.0526

1 300 41 000 31.5385

1 600 50 000 31.2500

2 200 68 000 30.9091

What do you think, is the data linear?

Let’s make a scatter plot.

Surprisingly, the data is linear, even if there is no fixed price per square foot!

PRICE = AA x SIZE + BB

PRICE = 30 x SIZE + 2 000

Scatter plots

SIZE [ft2] COST [$]

1 700 53 000

2 100 44 000

1 900 59 000

1 300 82 000

1 600 50 000

2 200 68 000

Draw scatterplot and tell me if these data are linear (i.e., do they lie in a line?).

outliers

Bar chart

SIZE [ft2] COST [$]

1 300 88 000

1 400 72 000

1 600 94 000

1 900 86 000

2 100 112 000

2 300 98 000

Warm up. Are these data linear?

No

How much to pay for a 2 200 ft2 house? Just simply interpolate.

105 000

Do you have trust in this number?

Bar chart• Take your data and pull them together.

Bar chart

SIZE [ft2] COST [$]

1 300 88 000

1 400 72 000

1 600 94 000

1 900 86 000

2 100 112 000

2 300 98 000

Bar chart• Much finer representation of the data• Bar chart allows you to understand global trends• Statistician uses cumulative tools (such as bar graph) to

gain the understanding of the underlying data.

Histograms• Special case of bar chart.• Bar chart looks at 2D data, histogram to 1D data. That is

the main difference.

132 784

137 192

122 177

147 121

143 000

126 010

129 200

124 312

128 132

Age distribution• Draw a histogram at the paper

with the bins by 10 years (i.e. 0-10, 11-20, …)

21

179

27

12

39

4

32

14

389

21

143

8 31

29

15

33

29

Věková pyramida

věková pyramida (strom života)

grafické znázornění věkové struktury obyvatelstva

source: http://cs.wikipedia.org/wiki/V%C4%9Bkov%C3%A1_pyramida

Histogram• Now I will collect heights of all of you in this room.

• Use Interactive Histogram Applet: http://www.shodor.org/interactivate/activities/Histogram/

• interval, bin

Histogram – Body fat• In Interactive Histogram Applet – choose „Body fat % in 252 men“

dataset.• Find reasonable bin size• Answer following questions. No matter of bin size what is always

true?

• Most scores fall around 20%.• The shape is roughly symmetrical.• Most scores fall in the middle of distribution.• There are more scores between 15 and 25 than between 35 and

50.• There are more scores between 0 and 10 than between 18 and 24.• Relatively more men have a body fat above 35% or below 5%.

Histogram – Income distribution• United States Census Bureau – http://www.census.gov

Income Number of houses

10 000 9401

20 000 14447

30 000 13642

40 000 12388

50 000 11028

Histogram – Income distribution

• This is an example of a (positively) skewed distribution (zprava zešikmené rozdělení).

• This distribution is not symmetrical.

• Most incomes fall to the left of the distribution.

Pie charts• koláčový graf

• elections• Party A – 50%• Party B – 50%

• Party A – 724 000 votes• Party B – 181 000 votes

A B C D E

Pie charts• Party A – 175 000• Party B – 50 000• Party C – 25 000• Party D – 50 000

• Please, draw the pie chart

A: 4/12B: 2/12C: 1/12D: 2/12

Bar chart and scatter plot• Which scatter plot corresponds to this bar chart?

Pie chart to histogram• Which histogram looks like it cames from the same data?