3. The concentration (in milligrams per litre) of a medication in a patient’s blood is
measured as time passes. Susan has collected the following data and is attempting to
express the concentration as a polynomial function of time.
Time
(x hours)
Concentration
(y mg/L)
0
1.5
3
4.5
6
7.5
9
0
26.9
41.2
47.8
46.0
36.8
20.3
a) Create a scatterplot of the data and use the quadratic regression feature to
determine the polynomial function, y = ax2 + bx + c, that best fits the data. Round
the parameters a, b, and c to two decimal places.
b) The doctor has decided that the patient needs a second dose of medication when
the concentration in the blood is less than 10mg/L. If the first dose of medication
was given at 9:00 a.m., at what time should the second dose be given?
4. A research student was investigating the relationship between job satisfaction, x, (as
measured by an employee on a scale from 1 to 10), and productivity, y, (as measured by
the employer on a scale of 1 to 100).
Data from 12 employees is given in the table.
Job Satisfaction
3
8
7
5
9
6
6
10
8
2
5
7
Productivity
44
81
75
66
90
70
71
98
75
25
68
77
a) The student looked at the scatterplot and suggested that the productivity could be
expressed as a linear function of job satisfaction. Perform a linear regression on
the data and determine a relationship in the form y = ax + b, giving a and b to two
decimal places.
b) Another student looked at the scatterplot and suggested that the relationship could
be represented by a cubic function with a point of inflection. Perform a cubic
regression on the data and determine a relationship in the form y = ax3 + bx2 + cx
+ d, giving a, b, c, and d to two decimal places.
c) Which model do you think best represents the data?