Question

a mathematics teacher wanted to see the correlation between test scores and homework. the homework grade (x) and test grade (y) are given in the accompanying table. write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 39.

Explanation:

Step1: Input data into calculator

Using a graphing calculator, input the \(x\) (homework grade) and \(y\) (test grade) values from the table.

Step2: Find linear regression equation

On the calculator, run the linear regression (\(Lin - Reg\)) function. The linear regression equation is of the form \(y = ax + b\). After calculation, \(a\approx0.77\) and \(b = 22.37\). So the equation is \(y=0.77x + 22.37\).

Step3: Predict test grade for \(x = 39\)

Substitute \(x = 39\) into the equation \(y=0.77x + 22.37\). Then \(y=0.77\times39+22.37\). First, calculate \(0.77\times39 = 30.03\). Then \(y=30.03+22.37=52.4\).

Answer:

The linear regression equation is \(y = 0.77x+22.37\). The projected test grade for a student with a homework grade of \(39\) is \(52\).