Question

Which regression model best fits the data set? (2,13), (4,8), (5,7.5), (7,9), (8,12)

A. linear

B. quadratic

C. exponential growth

D. exponential decay

Answer 1

The answer is quadratic.

Explanation:

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Answer 2

Quadratic Regression model best fits the data set.

Solution-

Taking x as input variable and y as output variable, regression models were obtained by using Excel.

As we can be seen that, the values of y is neither consistently increasing or decreasing ( as 13 > 8 > 7.5 < 9 < 12 ), so exponential growth and exponential decay are of no use (because exponential functions are monotonic functions, so either the are increasing or decreasing never both).

And also, it can not be linear, as the rate of change of y is not constant.

As we can obtain the correct regression model, by considering Co-efficient of Determination (R²). The value of R² ranges from 0 to 1. The more closer its value to 1, the better the regression model is.

From the attachment, it can be observed that,

`=0.006<<0.015<<0.995`

`=R^2_{\text{Exponential}}<<R^2_{\text{Linear}}<<R^2_{\text{Quadratic}}`

As the value of R² of the Quadratic Regression is more closer to 1, so that should be followed.