The document presents several analytical tasks involving the correlation and regression of construction-related data, such as the compressive strength of concrete mixed with varying percentages of nano metakaolin, the usage of cement bags in buildings, deflections of concrete beams under load, and the number of workers needed for construction over time. Specific calculations required include correlation coefficients, regression equations, and predictions for varying conditions. Additionally, it involves assessing partial and multiple correlations accounting for additional variables such as years of experience.

1. 1. The below table shows the Nano metakaolin Mixed with Concrete, X
Compressive strength of concrete, Y, per concrete cubes, for 7 different
percentages.
a. Find the correlation coefficient and interpret your result.
b. Find the equation of the regression line and predict the compressive
strength of the concrete cube of Nano Metakolin mixed with the
concrete at 18% and 23%
Nano metakaolin Mixed with
Concrete
Compressive strength of concrete
in N/mm2
0% 43.2
5% 43.7
10% 49.8
15% 51.2
20% 46.3
25% 39.5
2. The cements bags were used in different construction sites as shown in
below table.
a. Find the correlation coefficient and interpret your result.
b. Find the equation of the regression line and predict the number of
cement bags were used to construct 9th
,17th
and 20 floor buildings
Floors in Building Cement bags Required in No’s
5 100
8 125
10 133
12 146
15 159
18 172
3. The deflections of C 40 grade concrete beam by gradual loading condition as
shown in below table.

2. a. Find the correlation coefficient and interpret your result.
b. Find the equation of the regression line and predict the deflection of
the concrete beam at 30kN, 40kN and 45kN.
Load (kN)
Deflection (mm) of
C40 concrete beam
2.45 0.03
4.90 0.12
7.35 0.35
9.80 0.68
12.25 0.94
14.70 1.16
17.15 1.42
19.60 1.73
22.05 1.94
24.50 2.15
26.95 2.36
29.40 2.72
31.85 2.85
34.30 3.04
36.75 3.22
39.20 3.33
41.65 3.54
44.10 3.71
4. The construction work has completed in different places in different days.
The details were shown in below table.
a. Find the correlation coefficient and interpret your result.
b. Find the equation of the regression line and predict the number of
labors needs to complete the work at 153 days.
Works completed in Days No. of workers in site
30 23
45 26
60 31
75 29
90 33
105 27
120 23
135 28
150 17
165 19

3. 5. Calculate the partial (first-order) correlation between Working hours (Y) and
number of Workers (X), controlling for Workers Years of Experience (Z).
Buildings No. of workers
in site (X)
Working
hours of Site
Per Day (Y)
Years of Experience
(Z)
A 23 4 14
B 26 6 16
C 31 7 18
D 29 9 18
E 33 7 21
F 27 4 19
G 23 9 15
H 28 1 14
I 17 10 16
J 19 7 11
6. Calculate the Multiple correlations between Working hours (Y) and number
of Workers (X), controlling for Workers Years of Experience (Z).
Buildings No. of workers
in site (X)
Working
hours of Site
Per Day (Y)
Years of Experience
(Z)
A 23 4 14
B 26 6 16
C 31 7 18
D 29 9 18
E 33 7 21
F 27 4 19
G 23 9 15
H 28 1 14
I 17 10 16
J 19 7 11