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?