Short Answer 
To find the relationship between homework and test grades, use a tool like Excel for linear regression, resulting in an equation like y = 1.20x – 14.32. For estimating the homework grade based on a test score of 68, the homework grade calculated would be approximately 69.
Step 1: Use Technology for Linear Regression
To determine the regression equation that models the relationship between homework grade (x) and test grade (y), use a technology tool like Excel or a linear regression calculator. Input the data for homework grades and corresponding test grades into the tool. This will help in generating the linear equation in the format of y = bx + c.
Step 2: Understand the Components of the Equation
The regression equation obtained will typically be represented as y = 1.20x – 14.32. Here, b (the slope) is 1.20, indicating that for each point increase in homework grade, the test grade increases by 1.20 points. The intercept (c) is -14.32, representing the expected test grade when the homework grade is zero.
Step 3: Estimate Homework Grade for a Given Test Score
To estimate the homework grade based on a specific test score, plug in the value into the regression equation. For a test grade of 68:
- Set the equation: 68 = 1.20x – 14.32
- Add 14.32 to both sides: 82.32 = 1.20x
- Divide both sides by 1.20: x = 68.6
- Round to the nearest integer, yielding a homework grade of 69.