Question

Suppose a prediction equation was built on training data yielding:

y_hat = 145.5 -5.5*x
Given this small set of test data, calculate the RMSE.
x у
1 10.36 87.87
2 9.96 89.83
3 12.50 71.61
a. 1.98.
b. 3.04.
c. 9.21.
d. 5.37.

Answer 1

3.04

Explanation:

Given the prediction equation:

y_hat = 145.5 -5.5*x

- - - - x - - - - - - - - - у

1 - - 10.36 - - - - 87.87

2 - - 9.96 - - - - 89.83

3 - - 12.50 - - - - 71.61

1) y_hat = 145.5 -5.5*(10.36)

y_hat = 145.5 - 56.98 = 88.58

2) y_hat = 145.5 -5.5*(9.96)

y_hat = 145.5 - 54.78 = 90.72

3) y_hat = 145.5 -5.5*(12.50)

y_hat = 145.5 - 68.75 = 76.75

Root mean squared error (RMSE) :

Number of observations (n) = 3

√(Σ(y_hat - y)^2) / n

y_hat = predicted value

y = actual value

Σ[(88.58-87.87)^2+(90.72-89.83)^2+(76.75-71.61)]

Σ(0.71^2) + (0.89^2) + (5.14^2)

27.7158 / 3 = 9.2386

√9.2386

= 3.0395065

= 3.04