Q1: 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.

Region  Year       Line length (miles)           # of Faults.

Midlands             2000       15.6        15

Midlands             2001       15.6        18

North    2000       23.66     22

North    2001       23.66     16

South    2000       26.40     23

South    2001       26.40     18

East        2000       33.58     18

East        2001       33.58     28

West     2000       47.30     33

West     2001       47.30     27

Coast     2000       50.64     30

Coast     2001       50.64     27

(a) Does the data indicate that the number of faults per mile has changed from year 2000 to year 2001?

(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. Explain what this means in practical terms.