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 80.

homework grade (x) | test grade (y)
71 | 63
72 | 75
62 | 58
80 | 77
85 | 71
74 | 65
90 | 95
83 | 68
62 | 57

answer
regression equation:
final answer:

Explanation:

Step1: Input data into calculator

Input the \(x\) - values (homework grades: \(71,72,62,80,85,74,90,83,62\)) and \(y\) - values (test grades: \(63,75,58,77,71,65,95,68,57\)) into a statistics calculator.

Step2: Find the linear regression equation

Using the linear regression function on the calculator, we get the equation \(y = 0.9x - 1.1\) (rounded to the nearest tenth).

Step3: Predict the test grade for \(x = 80\)

Substitute \(x = 80\) into the equation \(y=0.9x - 1.1\). Then \(y=0.9\times80- 1.1=72 - 1.1 = 70.9\approx71\)

Answer:

Regression Equation: \(y = 0.9x-1.1\)
Final Answer: \(71\)