The linear regression equation that represents this set of data is Y = -12.41 + 1.15x and the projected test grade for a student with a homework grade of 49 is 44 and this can be determined by using the generalized equation of regression.
Given :
- 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.
The generalized regression equation is given below:
Y = a + bX --- (1)
where b is given by the formula:
[tex]\rm b = \dfrac{N\sum XY-\sum X \sum Y}{N\sum X^2-(\sum X)^2}[/tex]
Now, substitute the values of the known terms in the above formula in order to determine the value of 'b'.
b = 1.15
and the formula of a is given below:
[tex]\rm a = \dfrac{\sum Y - b \sum X}{N}[/tex]
Now, substitute the values of the known terms in the above formula in order to determine the value of 'a'.
a = -12.41
Now, substitute the values of a and b in the equation (1).
Y = -12.41 + 1.15x
Now, at x = 49 the value of Y becomes:
Y = -12.41 + 1.15(49)
Y = 43.94
Y [tex]\approx[/tex] 44
For more information, refer to the link given below:
https://brainly.com/question/7656407
