EDU10447 Applying Quantitative Concepts For Regression Analysis
Answer:
A local council surveyor is part of an environmental impact assessment team investigating possible residential development of two areas of land. The surveyor must determine if the two areas, Site 1 and Site 2, which run along existing creeks and roads, are the same surface area.
The aim of this section was to estimate the real surface area of the two sites.
Comparing the two relationships.
From the regression analysis, the R-Squared value for the species A is 0.7250; implying that 72.5% of the variation in the temperature is explained by species A.
On the other hand, the R-Squared value for the species B is 0.3503; implying that only 35.03% of the variation in the temperature is explained by species B.
The above findings clearly shows that the model involving species A is more effective in terms of determining the temperature as compared to the one involving species B.
|
|
Chirps per second | |
|
Temperature (oC) |
Species A |
Species B |
|
20.8 |
15.4 |
16.0 |
|
20.9 |
14.7 |
12.7 |
|
22 |
16.0 |
16.0 |
|
24 |
15.5 |
15.0 |
|
24.6 |
14.4 |
18.9 |
|
26.4 |
15.0 |
12.8 |
|
27 |
17.1 |
17.1 |
|
27 |
16.0 |
16.3 |
|
27.8 |
17.1 |
18.3 |
|
28.1 |
17.2 |
19.1 |
|
28.5 |
16.2 |
15.9 |
|
28.6 |
17.0 |
17.8 |
|
29.5 |
18.1 |
14.0 |
|
31.4 |
18.5 |
21.0 |
|
34.1 |
19.8 |
20.7 |
|
Australia |
Great Britain | |
|
Minimum |
5.00 |
11.00 |
|
1st Quartile |
13.75 |
17.25 |
|
Median |
23.00 |
22.00 |
|
3rd Quartile |
36.50 |
31.75 |
|
Maximum |
58.00 |
67.00 |
As can be seen, Australia has won a minimum of 5 medals with maximum number of medals being 58 while Great Britain has won a minimum of 11 medals with the maximum number of being 67 in all the Olympics that the two nations have attended. The interquartile range is 22.75 and 14.25 for Australia and Great Britain respectively.
Boxplot were further plotted to check on the distribution of the medals for the two nations, as can be seen, there seems to be outliers for the Great Britain but no outliers for Australia. This shows that Australia has been the most consistent nation in terms of overall performance.
Comparing performance of the two nations
A comparison of the performance of the two nations was done where we sought to check whether there is a significant difference in terms of the performance of the two nations for all the past Olympics. The hypothesis tested is as follows;
To test this, we used two-sample t-test and tested it at 5% level of significance. Results are given below;
|
t-Test: Two-Sample Assuming Equal Variances | ||
|
|
|
|
|
|
Australia |
Great Britain |
|
Mean |
26.16667 |
27.44444 |
|
Variance |
230.0294 |
274.8497 |
|
Observations |
18 |
18 |
|
Pooled Variance |
252.4395 |
|
|
Hypothesized Mean Difference |
0 |
|
|
df |
34 |
|
|
t Stat |
-0.24127 |
|
|
P(T<=t) one-tail |
0.405399 |
|
|
t Critical one-tail |
1.690924 |
|
|
P(T<=t) two-tail |
0.810797 |
|
|
t Critical two-tail |
2.032245 |
|
As can be seen, the p-value is given as 0.811 (a value greater than 5% level of significance), we thus fail to reject the null hypothesis and conclude that there is no significant difference in terms of the performance for the two nations.
Table 3.1 Total number of medals (including gold medals) won by Australian and British Olympic Athletes since World War II.
|
|
AUSTRALIA |
GREAT BRITAIN | ||
|
Olympics |
Gold |
TOTAL |
Gold |
TOTAL |
|
1948 London |
2 |
13 |
3 |
23 |
|
1952 Helsinki |
6 |
11 |
1 |
11 |
|
1956 Melbourne |
13 |
35 |
6 |
24 |
|
1960 Rome |
8 |
22 |
2 |
20 |
|
1964 Tokyo |
6 |
18 |
4 |
18 |
|
1968 Mexico |
5 |
17 |
5 |
13 |
|
1972 Munich |
8 |
17 |
4 |
18 |
|
1976 Montreal |
0 |
5 |
3 |
13 |
|
1980 Moscow |
2 |
9 |
5 |
21 |
|
1984 Los Angeles |
4 |
24 |
5 |
37 |
|
1988 Seoul |
3 |
14 |
5 |
24 |
|
1992 Barcelona |
7 |
27 |
5 |
20 |
|
1996 Atlanta |
9 |
41 |
1 |
15 |
|
2000 Sydney |
16 |
58 |
11 |
28 |
|
2004 Athens |
17 |
50 |
9 |
30 |
|
2008 Beijing |
14 |
46 |
19 |
47 |
|
2012 London |
8 |
35 |
29 |
65 |
|
2016 Rio De Janiero |
8 |
29 |
27 |
67 |
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