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: Enter data into calculator

Use a graphing calculator (e.g., TI - 84). Enter the \(x\) - values (homework grades: \(88,77,71,81,85,71,81,82,81\)) and \(y\) - values (test grades: \(82,73,71,71,70,63,82,79,78\)) into the list editor (\(L_1\) for \(x\) and \(L_2\) for \(y\)).

Step2: Calculate linear regression

Run the linear regression function (\(\text{LinReg}(ax + b)\)) on the calculator. The calculator will output \(a\approx0.32\) and \(b\approx47.72\). So the linear regression equation is \(y = 0.32x+47.72\).

Step3: Predict for \(x = 66\)

Substitute \(x = 66\) into the equation \(y=0.32x + 47.72\). Then \(y=0.32\times66+47.72\).

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Answer:

The linear regression equation is \(y = 0.32x + 47.72\). The projected test grade for a student with a homework grade of \(66\) is \(68\).