Statistická analýza dat Daniel 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 [$] 1 400 112 000 2 400 192 000 1 800 144 000 1 900 152 000 1 300 104 000 1 100 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 [$] 1 400 112 000 2 400 192 000 1 800 144 000 1 900 152 000 1 300 104 000 1 100 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? Look at data Program computers Run statistics software Drink beer

Linear relationship SIZE [ft2] COST [$] 1 400 98 000 2 400 168 000 1 800 126 000 1 900 133 000 91 000 1 100 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 PRICE SIZE

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, …) 29 27 14 21 12 9 17 14 32 3 39 9 4 33 38 21 31 29 8 15

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

Ktery odpovida temto datum? - E 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 udacity – Introduction to statistics – 5. Pie charts – Build a chart 4/12, 2/12, 1/12, 2/12 v poslednim prikladu pro Party A B C D A: 4/12 B: 2/12 C: 1/12 D: 2/12

Bar chart and scatter plot Which scatter plot corresponds to this bar chart? udacity – Introduction to statistics – Problem set 1: Visualization – Bar chart to Scatterplot – min: na konci videa Obrazek je na nasledujicim slidu.

Pie chart to histogram Which histogram looks like it cames from the same data? udacity – Introduction to statistics – Problem set 1: Visualization – Pie chart to Histogram – min: na konci videa Oba tyto grafy znazornuji frekvence. Obrazek je na nasledujicim slidu.