Question

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: Calculate the differences in \(y\) - values

For \(x = 1,y = 55\); \(x=2,y = 65\), the difference is \(65 - 55=10\).
For \(x = 2,y = 65\); \(x = 3,y = 75\), the difference is \(75 - 65 = 10\).
For \(x = 3,y = 75\); \(x = 4,y = 85\), the difference is \(85 - 75=10\).

Step2: Analyze the pattern

Since the change in \(y\) (test - score) is constant (\(\Delta y=10\)) for a constant change in \(x\) (hours studied, \(\Delta x = 1\)), the relationship follows a linear pattern \(y=mx + b\) where \(m=\frac{\Delta y}{\Delta x}=10\).

Answer:

A. Linear