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, estimate the homework grade, to the nearest integer, for a student with a test grade of 50.

Answer 1

The linear regression equation that represents this set of data is y = 4.83x - 173.51. For a student with a test grade of 50, the estimated homework grade is approximately 28.

Step-by-step explanation:

To write the linear regression equation, we use the equation y = mx + b, where m is the slope and b is the y-intercept. From the given equation ŷ - 173.51 + 4.83x, we can see that the slope is 4.83 and the y-intercept is -173.51. Therefore, the linear regression equation is y = 4.83x - 173.51.

To estimate the homework grade for a student with a test grade of 50, we substitute the test grade into the equation. y = 4.83(50) - 173.51 gives us a homework grade of approximately 28.