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# Correlation

1 (a) The following data was obtained for two variables, X & Y

X 135 110 130 145 175 160 120
Y 145 100 120 120 130 130 110

(i) Plot a scatter diagram for this data
(ii) Calculate the Pearson product moment correlation coefficient and the regression coefficients for this data
(iii) This data set seems to contain an outlier (that is, a pair of values which do not fit the trend shown by the remaining data). If this pair of values is excluded from the data, how will your answers to (ii) be affected?

(b) 12 soldiers were given instruction in marksmanship and a study was conducted to determine if the number of hours spend in practice shooting was related to proficiency.

The data is given in the table below:

Soldier Hours of Practice Proficiency Rating
1 24 75
2 23 83
3 19.5 98
4 18 80
5 17 74
6 16.5 69
7 16 71
8 15 68
9 14.5 59
10 14 62
11 13.5 70
12 10 54

Calculate the correlation coefficient for this data.

(c ) The following scores were obtained by 5 student on two tests.

Student Test X Test Y
A 5 1
B 5 3
C 5 5
D 5 7
E 5 9

Calculate the Pearson product moment correlation coefficient and the spearman rank correlation coefficient.

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See attached file for full problem description)

Full detailed workings are required with excel/graphical attachments where required.

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#### Solution Summary

Calculates Pearson product moment correlation coefficient and the spearman rank correlation coefficient.

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