Question

The table shows the weights (in pounds) and the prescribed dosages (in milligrams) of medicine for six patients.

Weight (lb), x Dosage (mg), y
94 72
119 90
135 103
150 115
185 140
202 156
a. Find an equation of the line of best fit. Round the slope and the y -intercept to the nearest tenth, if necessary.

y=
Question 2
Identify the correlation coefficient. Round your answer to the nearest thousandths.

Question 3
Interpret the correlation coefficient.
0 / 10000 Word Limit
Question 4
b. Interpret the slope of the line of best fit.

Question 5
c. A patient who weighs 140 pounds is prescribed 135 milligrams of medicine. How does this affect the line of best fit? Explain.

Answer 1

(A) Using calculator, the equation of the line of best fit is y=0.77x-1.1y=0.77x−1.1 and correlation coefficient is 0.9990.999

The relationship is strongly positive as correlation coefficient is very close to +1.

Step 2

(B) The slope of best fit gives the change in dosage for a unit (lb) increase in weight of patient. We find that the dosage increases by about 0.77 mg for a unit increase in weight of patient.

Step 3

(C) Adding observation (140, 135)(140,135) to the data set. the regression line changes to y=6.12+0.75xy=6.12+0.75x. It increases the intercept but decreases slope.

But the correlation falls to 0.9340.934, weakening the relationship. This happens as the observation is an outlier.

Result

a. y=0.77x-1.1y=0.77x−1.1, strong positive relationship

b. represents change in dosage for a unit increase in weight

c. regression line changes to y=6.12+0.75xy=6.12+0.75x.