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The linear regression equation based on the data provided is:

\[
y = 1.4x - 35.5
\]

Using this equation, the projected test grade for a student with a homework grade of 55 is:

\[
y = 1.4(55) - 35.5 = 42
\]

So, the projected test grade is **42**.

Do you need further details or have any questions? Here are five related questions to expand your understanding:

1. How is the slope of a linear regression equation interpreted in this context?
2. What does the intercept of the regression line represent?
3. How is the coefficient of determination (R²) useful in evaluating a regression model?
4. Can we use this linear model to predict test scores for homework grades outside the given range?
5. How does rounding affect the accuracy of the predicted results?

**Tip**: Always check the correlation coefficient to see how well the regression line fits the data.

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 55.

Learn how to calculate the linear regression equation based on the correlation between homework grades and test scores. The problem involves rounding coefficients to the nearest tenth and finding the projected test grade for a homework grade of 55. Suitable for high school students in Grades 10-12.

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