Answer to Question #110142 in Statistics and Probability for suresh

Question

Use Linear Regression to find the slope-intercept formula for the best line passing through the following points:
x y
-2 7.398704
-1 10.79976
0 2.172701
1 7.447045
2 1.954988
3 -1.85296
4 -0.41138
5 -6.87151
6 -11.3635
7 -13.711
8 -13.6287
9 -21.6955
10 -15.7112
Equation for Best Line:
A) y = 2.5246*x - 5.8311
B) y = -5.8311*x + 2.5246
C) y = -2.5246*x + 5.8311
D) y = 5.8311*x - 2.5246

Answer 1

$Y=a+bx$

$a=\frac{(\sum y \sum x^2)-(\sum x \sum xy)}{n\sum x^2-(\sum x)^2}$

$a=\frac{(-55.4726×390)-(52×(-681.361))}{(13×390)-52^2}=5.8311$

$b=\frac{n\sum xy-\sum x \sum y}{n\sum x^2-(\sum x)^2}$

$b=\frac{(13×(-681.361))-(52×(-55.4726))}{(13×390)-52^2}=-2.5246$

Thus, $Y=5.8311-2.5246x$

The correct choice is (c).