Question

A student who has created a linear model is disappointed to find that herR2 value is a very low 13%. a) Does this mean that a linear model is not appropriate? Explain. b) Does this model allow the student to make accurate predictions? Explain.

Answer 1

a) No it doesn't mean that linear model is inappropriate

b) No. The prediction using this model will not be accurate.

Explanation:

a)

For answering this part, firstly consider the concept of
`R^(2)`

The
`R^(2)` also known as coefficient of determination is used to determine the amount of variability in dependent variable is explained by the linear model. Lower
`R^(2)` depicts that less variation of dependent is explained by the independent variable using the linear model. The linearity of model is determined by scatter plot. Thus, if the
`R^(2)` is lower, it doesn't mean that linear model is inappropriate.

b)

The predictions made by the model having lower
`R^(2)` value are erroneous. The model is used for prediction if the linear model explains the larger portion of variability in dependent variation. If the predictions made from the model that have lower
`R^(2)` value then the predicted values will not be close to the actual value and thus residuals will not be minimum as residuals are the difference of actual and predicted values.