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 tenth. using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 74.

homework grade (x) test grade (y)
78 73
51 54
62 49
79 67
71 58
78 66
84 73
57 51

copy values for calculator
open statistics calculator

answer
regression equation:
final answer:

Explanation:

Step1: Use a calculator for linear regression

Input the \(x\) (homework grade) and \(y\) (test grade) values into a statistics calculator.

Step2: Obtain the regression equation

The linear regression equation has the form \(y = ax + b\). After calculation, \(a\approx0.7\) and \(b = 13.8\). So the equation is \(y=0.7x + 13.8\).

Step3: Predict the test grade

Substitute \(x = 74\) into the equation \(y=0.7x + 13.8\). Then \(y=0.7\times74+13.8=51.8 + 13.8=65.6\). Rounding to the nearest integer gives \(y = 66\).

Answer:

Regression Equation: \(y = 0.7x+13.8\)
Final Answer: \(66\)