Exponential Modelling Question

Question

A tour guide noticed that larger groups took more time to assemble for an event. The guide collected the data below

Number of People 2, 3, 4, 5, 6, 7, 8, 9, 10

Time to Assemble(Minutes) 2, 2.6, 3.4, 4.4, 5.7, 7.4, 9.7, 12.5, 16.3

Use a statistical utility (DESMOS, a graphing calculator, MS Excel, Google Sheets, etc.) to make a scatterplot.

Round all answers to 4 decimal places. Do not write decimal places if it is a whole number. For example, write 3 and not 3.0000.

Find the linear regression model: y = Answer(x) - Answer

What is the correlation coefficient of this linear regression model: Answer

Find the exponential regression model: f(x) = Answer(answer)^x

What is the correlation coefficient of the exponential model: Answer

Which of these two models seems to fit the data better (answer linear or exponential): Answer

Answer 1

Hello,

Using MS Excel:

Whenever you want to determine which regression "Best Fits" the data, you want an R² (a.k.a Correlation Coefficient) as close to 1 as possible. With the exponential correlation coeffient being exactly 1, this is the absolute best fit line without getting into more complex regression formlas.