Respuesta :
Answer:
The regression equation is:
Final Grade = 96.14 - 2.76 Number of absence
A student who was absent for 14 days received a final grade of 58.
Step-by-step explanation:
The general form a regression equation is:
[tex]y=\alpha +\beta x[/tex]
Here,
y = dependent variable = Final grade
x = independent variable = Number of absence
α = intercept
β = slope
The formula to compute the intercept and slope are:
[tex]\alpha =\frac{\sum Y. \sum X^{2}-\sum X.\sum XY}{n.\sum X^{2}-(\sum X)^{2}}[/tex]
[tex]\beta =\frac{n.\sum XY-\sum X.\sum Y}{n.\sum X^{2}-(\sum X)^{2}}[/tex]
The value of α and β are computed as follows:
[tex]\alpha =\frac{\sum Y. \sum X^{2}-\sum X.\sum XY}{n.\sum X^{2}-(\sum X)^{2}}=\frac{(722\times460-(52\times3732)}{(9\times460)-(52)^{2}} =96.139\approx96.14[/tex]
[tex]\beta =\frac{n.\sum XY-\sum X.\sum Y}{n.\sum X^{2}-(\sum X)^{2}}=\frac{(9\times3732-(52\times722)}{(9\times460)-(52)^{2}} =-2.755\approx-2.76[/tex]
The regression equation is:
Final Grade = 96.14 - 2.76 Number of absence
For the value of Number of absence = 14 compute the value of Final grade as follows:
[tex]Final\ Grade = 96.14 - 2.76\ Number\ of\ absence\\=96.14-(2.76\times14)\\=57.5\\\approx58[/tex]
Thus, a student who was absent for 14 days received a final grade of 58.
