Question

Age (years) 10 20 30 40 50 60 Time (minutes) 13 16 11 16 14 22 —10. A group of six dentists were comparing how long they spend on initial examinations based on the age of their patients. The table shows the data points for the six dentists. Using technology, the equation of the best fit line was found to be û = 0.1257x + 10.93. Which calculation correctly determines the residual for the time spent on the initial examination of a 40-year-old patient? (A.) Ý40 = 0.1257 + 10.93(40) = 37.3257; 37.3257 – 40 = -2.6743 (B.) Ý40 = 0.1257 + 10.93(40) = 37.3257; 40 - 37.3257 = 2.6743 (C.) Ý40 = 0.1257(40) + 10.93 = 15.958; 16 - 15.958 = 0.042(D.) Ý40 = 0.1257(40) + 10.93 = 15.958; 15.958 - 16 = -0.042

Answer 1

In the equation:

y = 0.1257x + 10.93

y represents time (in minutes) and x represents age (in years)

Residual value = actual value - predicted value

The actual value for a 40 years old patient is: 16 minutes

The predicted value for a 40 years old patient is: 0.1257*40 + 10.93 = 15.958 minutes

Then, the residual value is 16 - 15.958 = 0.042 minutes (option C)