Question

I struggled with classes English, Biology, Geometry and History ever since I started all the way back in high school. The Biology class in college is not any different than the other classes. I predict the more hours I put into my studying it will amplify my comprehension of these classes. Below is how many times I spend in the classes I take a day each week, which is x. The other is the amount of hours I study which is y.

Class, x Hours, y

3 2

2    2

3    4

1    5

4    1

Discuss the meaning of the standard error of the estimate and how it affects the predicted values of Y for that analysis.

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
3	2	0.16	0.64	-0.32
2	2	0.36	0.64	0.48
3	4	0.16	1.44	0.48
1	5	2.56	4.84	-3.52
4	1	1.96	3.24	-2.52

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	13.00	14.00	5.20	10.80	-5.40
mean	2.60	2.80	SSxx	SSyy	SSxy

SSE=   (SSxx * SSyy - SS²xy)/SSxx =    5.1923
      
std error of estimate ,Se =    √(SSE/(n-2)) =    1.3156

The standard error of the regression (S), also known as the standard error of the estimate, represents the average distance that the observed values fall from the regression line. Conveniently, it tells you how wrong the regression model is on average using the units of the response variable. Smaller values are better because it indicates that the observations are closer to the fitted line.