A study on the occurrence of line faults in an electricity supply network was carried out over a two-year period. Data was collected from six regions on the number of faults per year in each of the two years, and gave the results shown in the table below.
|
(a) Region
|
(b) Year
|
Line length (miles)
|
# of Faults.
|
|
Midlands
|
2008
|
15.6
|
15
|
|
Midlands
|
2009
|
15.6
|
18
|
|
North
|
2008
|
23.66
|
22
|
|
North
|
2009
|
23.66
|
16
|
|
South
|
2008
|
26.40
|
23
|
|
South
|
2009
|
26.40
|
18
|
|
East
|
2008
|
33.58
|
18
|
|
East
|
2009
|
33.58
|
28
|
|
West
|
2008
|
47.30
|
33
|
|
West
|
2009
|
47.30
|
27
|
|
Coast
|
2008
|
50.64
|
30
|
|
Coast
|
2009
|
50.64
|
27
|
(a) Does the data indicate that the number of faults per mile has changed from year 2008 to year 2009?
(b)Draw the graph relating Number of Faults to Line length.
(c) Does the data support the suggestion that the two variables (# Faults and Line length) are related? If so, find the relationship between them and state the probable limits of the Regression Coefficient with 95% confidence.
(d) Test the hypothesis that the graph should pass through the origin (i.e. a = 0). Explain what this means in practical terms.