Practicals 9: Regression, correlation and general linear models
1. Snowflakes can have very different sizes and this might to depend on the temperature of the ice
crystals from which they are formed. In winter 2012, mean snowflake size and ice crystals
temperature were recorded during 14 snowing events in České Budějovice. The resulting data are
summarized in table below:
Sbowing event No. mean snowflake ice
crystal temperature [°C]
mean snowflake
diameter [mm]
1 -18 4.9
2 -20 6.1
3 -5 8.3
4 -12 8
5 -8 8.7
6 -9 8.5
7 -2 10.2
8 -14 7.1
9 -8 8.4
10 -17 6.2
11 -2 9.9
12 -4 9.3
13 -3 11
14 -12 7.6
How does the snowflake size depend on temperature?
Perform a statistical analysis, support it by a figure and present a conclusion.
In addition to the statistical model, report the regression equation describing the dependence of
snowflake size on temperature.
What can we say about the snowflake size at the temperature 5°C?
2. Intelligence Quotient (IQ) of Czech Ministry of Interior Affairs employees was measured. These
people were also asked on the average amount of beer they drink daily. The results were following:
Is the amount of beer consumed correlated with intelligence of Czech Ministry of Interior Affairs
employees?
IQ beer [liters]
69 2
84 3.5
95 4.6
98 1.2
65 8
105 1.1
87 2.3
91 3.2
94 1
111 0.5
110 8
75 1
A. Dependence of THC concentration in blood on the amount of cannabis smoked was analyzed in
one person who smoked different amounts of dried cannabis of the same source. The intervals
between measurements were long enough to decrease of THC concentration to 0 before each trial.
Does THC concentration depend on the amount of cannabis smoked?
Perform a statistical analysis and illustrate it with a figure.
B. 20 books published in recent year were randomly selected in a bookshop. Number of pages were
counted for each book and the age of the author was retrieved.
The resulting data were as following:
author age number of pages
57 568
41 302
23 102
56 574
85 600
57 162
74 128
85 405
61 201
35 129
38 204
62 305
45 450
41 275
43 320
75 401
56 230
51 222
31 188
48 196
Does the author age have an affect on thickness of books?
THC [mg/litre blood] Cannabis DW [g]
10.1 5.3
3 1.2
8.7 3.8
12.3 8.5
20.8 9.1
5.9 3.1
10.1 4.5
12.3 8.5
5.9 6.5
10.1 7.8
Perform a statistical analysis and illustrate it with a figure.
C. Relationship between mean age of children in a family and height of Christmas tree was studied.
The resulting data were following
Does the age of children in family affect the height of the Christmas tree bought by the parents?
D. During a field survey 10 frogs were captured, measured (body length and body mass) and
released.
Following data were obtained:
Frog body mass [g] body length [mm]
1 7 56
2 10 71
3 11 80
4 8 53
5 9 61
6 14 91
7 8 64
8 11 79
9 12 85
10 8 62
Is there any correlation between body mass and length in frogs? What is the proportion of
variability shared by the two variables?
tree height [m] age [yrs]
2.2 3.5
3.1 4.2
0.8 15.8
2.5 7.6
1.4 12.8
1.7 16.4
1.2 15.3
2.8 6.5
0.9 19.5
1.6 5.6