Question

A model with explanatory variable x and response variable y takes the form:

y-hat = a1 + a2x

where y-hat is the predicted value of the value of y

when the explanatory variable takes the value x

1. To fit the model by the criteria of the root-mean-squared-deviation, we seek values of a1 and a2 to make what as small as possible?

a. the sum of differences between predicted values y-hat and observed values y.

b. the sum of absolute differences between predicted value y-hat and observed values y.

c. the average squared differences between predicted values y-hat and observed values y.

d. the sum of horizontal distances between points and the line of the predicted values.

Answer 1

To fit the model by the criteria of the root-mean-squared-deviation, we seek values of a1 and a2 to make what as small as possible:-

the average squared differences between predicted values y-hat and observed values y.(C)

[ the root-mean-square deviation (RMSD) is a frequently used measure of the differences between values predicted by a model and the values observed.  generally, a lower RMSD is better than a higher RMSD.

RMSD is the square root of the average of squared errors and is denoted as:-

where, n = number of observation,

= predicted value of y from the model

y = observed value ]

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