Question

1. the table shows the relationship between hours studied and test scores. hours studied (x) test score (y) 1 55 2 65 3 75 4 85 what type of regression model best fits this data? a) linear b) quadratic c) exponential

Explanation:

Step1: Check the change in \(y\) values

When \(x = 1,y = 55\); when \(x=2,y = 65\) (change \(y_2 - y_1=65 - 55 = 10\)); when \(x = 3,y = 75\) (change \(y_3 - y_2=75 - 65 = 10\)); when \(x = 4,y = 85\) (change \(y_4 - y_3=85 - 75 = 10\)). The change in \(y\) (test - score) for a unit change in \(x\) (hours studied) is constant (\(\Delta y=10\) for \(\Delta x = 1\)).

Step2: Recall regression - model characteristics

• Linear regression: Has a constant rate of change. The general form is \(y=mx + b\), where \(m\) (slope) is the rate of change.
• Quadratic regression: Has the form \(y = ax^{2}+bx + c\) and the rate of change of \(y\) with respect to \(x\) is not constant.
• Exponential regression: Has the form \(y = a\cdot b^{x}\) and the relative change (\(\frac{\Delta y}{y}\)) is constant, not the absolute change (\(\Delta y\)).

Answer:

A. Linear