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 66.

Explanation:

Step1: Input data into calculator

Using a calculator (such as TI - 84 Plus), enter the \(x\) values (homework grades: \(88,77,71,81,85,71,81,82\)) and \(y\) values (test grades: \(82,73,71,71,70,63,82,79\)) into the list editor (\(L_1\) for \(x\) and \(L_2\) for \(y\)).

Step2: Calculate regression equation

Run the linear regression \(LinReg(ax + b)\) function on the calculator. The calculator will output the values of \(a\) (slope) and \(b\) (y - intercept). After calculation, \(a\approx0.62\) and \(b = 20.33\). So the regression equation is \(y=0.62x + 20.33\).

Step3: Predict test grade

Substitute \(x = 66\) into the regression equation \(y=0.62x + 20.33\). Then \(y=0.62\times66+20.33=40.92 + 20.33=61.25\approx61\).

Answer:

The linear regression equation is \(y = 0.62x+20.33\), and the projected test grade for a student with a homework grade of \(66\) is \(61\).