Answer
a) Predicted distance covered by the golfball for a club-head speed of 100 mph = 260.8 yards
b) Residual of the observed value of 265 yards is 4.2 yards.
Step-by-step explanation
We have been given a relation that relates the club-head speed in miles per hour, x, to the distance covered by the golf ball in yards, y.
y = 2.8333x - 22.4967
a) We are then asked to find the distance covered by the golf ball for a club-head speed of 100 miles per hour.
That is, we need to find y when x = 100
y = 2.8333x - 22.4967
y = 2.8333 (100) - 22.4967
y = 283.33 - 22.4967
y = 260.8333 yards = 260.8 yards to the nearest tenth.
b) We are then told that the actual distance covered by the golfball for a club-head speed of 100 miles per hour is 265 yards.
We are then asked to find the residual of the observed value.
The residual of an observed value is the difference between the observed value and the predicted value of the quantity of interest.
For this question,
Observed value = 265 yards
Predicted or estimated value = 260.8 yards
Residual = (Observed value) - (Predicted value)
Residual = 265 - 260.8
Residual = 4.2 yards
Hope this Helps!!!