Question

X (input)	Y (output)
2	26.457
2.4	28.254
2.6	32.287
3.2	45.354
3.6	53.925
3.8	67.066
4.2	82.364
4.5	91.317
4.8	102.530
5.2	127.204
5.7	153.953
6.2	191.203
6.4	174.886
6.7	188.946
6.9	203.006

Consider the dataset between a quantitative input variable, ? and a quantitative response (output) variable, ?. Which of the following provides an optimal fit between them - a linear model, a complete quadratic model or a complete third order model? (Hint: You can use adjusted multiple coefficient of determination, ?? 2 to determine the optimal model.

Your answers below must be accompanied by appropriate computation in Excel)

?? 2 value for the linear model = ________________

?? 2 value for the quadratic model = ________________

?? 2 value for the third order model = ________________

Therefore, the optimal model is Linear, Quadratic or Third-order

Answer 1

Fitting a linear trendline through the data in Excel (right click on the graph -> Add trendline -> Linear -> Show R-squared value on chart), we get the following:

Now, fitting a quadratic model similarly in Excel, we get the following:

Finally, fitting a third order model, we get the following chart:

R-squared for:

Linear model: 09698

Quadratic model: 0.9863

Third order model: 0.9922

Hence, the third order model looks to be model (given it has highest R-squared, the input variable X explains the variability in output variable Y to the greatest extent in the third order model).