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

Use a graphing calculator or statistical software. Input the \(x\)-values (homework grades: \(75,82,89,90,78,60,76,50\)) and \(y\)-values (test grades: \(64,80,93,84,66,64,74,55\)).

Step2: Calculate linear regression equation

On a TI - 84 Plus (for example), go to STAT > CALC > LinReg(a + bx). The calculator will output \(a\approx26.32\) and \(b\approx0.68\). So the linear regression equation is \(y = 0.68x+26.32\).

Step3: Predict for \(x = 39\)

Substitute \(x = 39\) into the equation \(y=0.68x + 26.32\). Then \(y=0.68\times39+26.32\).
First, calculate \(0.68\times39=26.52\).
Then \(y=26.52 + 26.32=52.84\).

Answer:

The linear regression equation is \(y = 0.68x+26.32\). The projected test grade for \(x = 39\) is \(53\).