Practicals 9: Regression, correlation, and general linear models
1. Snowflakes can have very different sizes, which might depend on the temperature of the ice
crystals from which they are formed. In winter 2021, mean snowflake size and ice crystal
temperature were recorded during 14 snowing events in Brno. The resulting data are summarized in
the table below:
Snowing event No. mean snowflake ice
crystal temperature (°C)
mean snowflake
diameter (mm)
1 -18 6.9
2 -20 7.1
3 -5 8.5
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 10.2
14 -12 7.6
How does the snowflake size depend on temperature?
Perform a statistical analysis, support it with 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 5°C?
2. The Intelligence Quotient (IQ) of Czech Ministry of Interior Affairs employees was measured.
These people were also asked about the average amount of beer they drink daily. The results were
as follows:
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
Is the amount of beer consumed correlated with the intelligence of Czech Ministry of Interior
Affairs employees?
3. 530 School children took part in a swimming competition. Their height was also measured in
addition to swimming speed. Is swimming speed significantly affected by children height?
The data are available in Excel spradsheed on sheet 3.
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 from the same source. The intervals
between measurements were long enough to decrease of THC concentration to 0 before each trial.
Smoking event THC (mg/ l blood) Cannabis DW (g)
1 10.1 5.3
2 3 1.2
3 8.7 3.8
4 12.3 8.5
5 20.8 9.1
6 5.9 3.1
7 10.1 4.5
8 12.3 8.5
9 5.9 6.5
10 10.1 7.8
Does THC concentration in the blood depend on the amount of cannabis smoked?
Perform a statistical analysis and illustrate it with a figure.
B. 20 books published in recent years were randomly selected in a bookshop. The numbers of pages
were counted for each book and the age of the author was retrieved. The resulting data were as
follows:
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's age have an effect on the thickness of books?
Perform a statistical analysis and illustrate it with a figure.
C. The relationship between the mean age of children in a family and the height of the Christmas
tree was studied. The resulting data were the following:
tree height (m) age
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
Does the age of children in the 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. The 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?
E. The relationship between car mass and fuel consumption was studied. The resulting data are
summarized in the table below.
car mass (kg) fuel consumption (liter per 100km)
1540 6.5
1100 4.7
1230 4.3
2410 5.9
1890 6.5
1220 5.3
1080 4.7
2340 7.1
3030 7.8
1930 8.2
1460 5.6
Does the fuel consumption depend on car mass? Perform a statistical analysis and illustrate it by a
figure.