Answer:
The homework grade, to the nearest integer, for a student with a test grade of 68 is 69.
Step-by-step explanation:
The general form of the linear regression equation is:
[tex]y=a+bx[/tex]
Here,
y = dependent variable = test grade
x = independent variable = homework grade
a = intercept
b = slope
Compute the value of a and b as follows:
[tex]a=\frac{\sum Y\cdot \sum X^{2}-\sum X\cdot\sum XY}{n\cdot \sum X^{2}-(\sum X)^{2}}\\\\=\frac{(592\times 44909)-(591\times45227)}{(8\times44909)-(591)^{2}}\\\\=-14.316[/tex] [tex]b=\frac{n\cdot \sum XY-\sum X\cdot\sum Y}{n\cdot \sum X^{2}-(\sum X)^{2}}\\\\=\frac{(8\times 45227)-(591\592)}{(8\times44909)-(591)^{2}}\\\\=1.195[/tex]
The linear regression equation that represents the set of data is:
[tex]y=-14.316+1.195x[/tex]
Compute the value of x for y = 68 as follows:
[tex]y=-14.316+1.195x[/tex]
[tex]68=-14.316+1.195x\\1.195x=68+14.316\\1.195x=82.316\\x=68.884\\x\approx 69[/tex]
Thus, the homework grade, to the nearest integer, for a student with a test grade of 68 is 69.
