A study is made for particular allergy medication in order to determine the length of relief it provides, y (in hours), in relation to the dosage of medication, x (in mg). For this reason, ten patients were given different doses of the medication and were asked to report back when the medication seemed to wear off.

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A study is made for particular allergy medication in order to determine the length of relief it provides, y (in hours), in relation to the dosage of medication, x (in mg).
For this reason, ten patients were given different doses of the medication and were
asked to report back when the medication seemed to wear off.

A study is made for a particular allergy medication in order to determine the length
of relief it provides, y (in hours), in relation to the dosage of medication, x (in mg).
For this reason, ten patients were given different doses of the medication and were
asked to report back when the medication seemed to wear off.
Patient
#1 #2 #3 #4 #5
#6
#7
#8
#9 #10
Dosage (x)
Relief Hours (y) | 9.1
3
3.5
4
5
6.5
7
8
8.5
9
5.5
12.3 9.2 14.2
16.8 22.0
18.3 24.5 22.7
The summary statistics for these data are:
Sum of x data: 60.5
Sum of the squares of x data: 406.75
Sum of y data: 154.6 | Sum of the squares of y data: 2,767.3
Sum of the products of x and y data: 1,049.1
(a)
i. Draw a scatter diagram of these data. Label the diagram carefully.
ii. Calculate the sample correlation coefficient. Interpret your findings.
iii. Calculate the least squares line of y on x and draw the line on the scatter
diagram.
iv. Suppose that you observe more data and when you draw the corresponding
scatter diagram a non-linear association is revealed. Discuss how this can
be interpreted in the context of the problem.
Transcribed Image Text:A study is made for a particular allergy medication in order to determine the length of relief it provides, y (in hours), in relation to the dosage of medication, x (in mg). For this reason, ten patients were given different doses of the medication and were asked to report back when the medication seemed to wear off. Patient #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 Dosage (x) Relief Hours (y) | 9.1 3 3.5 4 5 6.5 7 8 8.5 9 5.5 12.3 9.2 14.2 16.8 22.0 18.3 24.5 22.7 The summary statistics for these data are: Sum of x data: 60.5 Sum of the squares of x data: 406.75 Sum of y data: 154.6 | Sum of the squares of y data: 2,767.3 Sum of the products of x and y data: 1,049.1 (a) i. Draw a scatter diagram of these data. Label the diagram carefully. ii. Calculate the sample correlation coefficient. Interpret your findings. iii. Calculate the least squares line of y on x and draw the line on the scatter diagram. iv. Suppose that you observe more data and when you draw the corresponding scatter diagram a non-linear association is revealed. Discuss how this can be interpreted in the context of the problem.
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