Question

by visual inspection, determine the best - fitting regression model for the scatterplot.
a. linear
b. exponential
c. no pattern
d. quadratic

Explanation:

Step1: Analyze linear model

A linear model \(y = mx + b\) would form a straight - line pattern. The given scatter - plot does not show a straight - line trend.

Step2: Analyze quadratic model

A quadratic model \(y=ax^{2}+bx + c\) has a parabolic shape (either opening up or down). The given scatter - plot does not show a parabolic trend.

Step3: Analyze no - pattern model

If there was no pattern, the points would be randomly scattered with no discernible increase or decrease trend. Here, there is a trend of rapid decrease.

Step4: Analyze exponential model

An exponential model \(y = ab^{x}\) (\(b>1\) for growth and \(0 < b<1\) for decay) shows a rapid increase or decrease. The scatter - plot shows a rapid decrease which is characteristic of an exponential decay model (\(y = ab^{x},0 < b<1\)).

Answer:

B. Exponential