Question

The following data show the length of the coasters at the Mega Park (x) and height of the same coasters (y). The regression equation for the data is given by y = 21.94 + 0.018x

Length	Height
1377	49
4424	112
3403	80
2780	45
3196	90
2000	41
790	28
2671	50
3450	100
2037	80
2134	80
679	28
1214	50
6072	120

a.      State and interpret the slope in the context of this problem, given the regression equation above.

b.      How tall does the linear regression model predict a coaster of 3450 feet long will be?

c.       Find and interpret the residual for the coaster which is 3450 feet long and has a height of 100 feet?

Answer 1

a) The regression equation here is: y = 21.94 + 0.018x
Height = 21.94 + 0.018*Length

The interpretation of the slope here is that for a unit increase in the length of the coaster there would be a 0.018 units increase in the height of coaster expected.

b) The predicted value here is computed as:

Height = 21.94 + 0.018*Length

Height = 21.94 + 0.018*3450 = 84.04

Therefore 84.04 feet is the predicted value of coaster length here.

c) As the real height here is 100ft, the residual is computed here as:

Residual = observed value - Predicted value

Residual = 100 - 84.04 = 15.96

Therefore 15.96 is the required residual value here. The interpretation of this is that we are predicting the height 15.96 points lower from the real point.