A golf ball is dropped from 15 different heights (in inches) and the height of the bounce is recorded (in inches.) The regression analysis gives the model
y-hat = -0.4 + 0.70 (drop height)
where y-hat is the predicted bounce height of the golf ball.
A golf ball dropped from 71 inches bounced 53.3 inches. What is the residual for this bounce height.?
I am having trouble setting up the problem to get an answer...
Gfh
To find the residual for a specific data point in regression analysis, you need to subtract the predicted value (y-hat) from the actual value. In this case, the predicted bounce height (y-hat) is given by the regression model as y-hat = -0.4 + 0.70 (drop height).
Given that the drop height is 71 inches and the bounce height is 53.3 inches, we can plug these values into the regression model to find the predicted bounce height (y-hat):
y-hat = -0.4 + 0.70 (71)
= -0.4 + 49.7
= 49.3 inches
Now, to find the residual, subtract the predicted bounce height (y-hat) from the actual bounce height:
Residual = Actual Bounce Height - Predicted Bounce Height
= 53.3 - 49.3
= 4 inches
Therefore, the residual for this bounce height is 4 inches.
To find the residual for the given bounce height of 53.3 inches, we need to calculate the difference between the actual bounce height and the predicted bounce height.
Given:
Actual bounce height (y) = 53.3 inches
Predicted bounce height (y-hat) = -0.4 + 0.70 (drop height)
We have the information that the ball was dropped from a height of 71 inches.
Substituting the values in the equation y-hat = -0.4 + 0.70 (drop height):
y-hat = -0.4 + 0.70 (71)
y-hat = -0.4 + 49.7
y-hat = 49.3
Now, we can calculate the residual by subtracting the predicted bounce height from the actual bounce height:
Residual = Actual bounce height - Predicted bounce height
Residual = 53.3 - 49.3
Residual = 4
Therefore, the residual for this bounce height is 4 inches.