Question

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

Answer 1

Answer-

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 in exponential function the growth or decay rate is constant).

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,

$=0.006$

$=R^2_{\text{Exponential}}$

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