Question

In: Math

2. Consider the following data: x= 1, 2, 3, 4, 5 y =3, 2, 4, 6,...

2. Consider the following data:

x= 1, 2, 3, 4, 5

y =3, 2, 4, 6, 5

By hand, not using Matlab, and showing your work:

(a) Compute the correlation coefficient.

(b) Find the least-squares line.

(c) Find the standard deviation around the least-squares line.

Expert Solution

(a) The correlation coefficient is 0.8.

(b) The least-squares line is:

y = a + bx = 1.6 + 0.8x

(c) Standard deviation = 1.58

The calculations are:

	x	y	(x-xMean)	(y-yMean)	(x-xMean)*(y-yMean)	(x-xMean)²	zx	zy	zx*zy
	1	3	-2	-1	2	4	-1.26491	-0.63246	0.8
	2	2	-1	-2	2	1	-0.63246	-1.26491	0.8
	3	4	0	0	0	0	0	0	0
	4	6	1	2	2	1	0.632456	1.264911	0.8
	5	5	2	1	2	4	1.264911	0.632456	0.8
Mean	3	4	0	0	8	10			3.2
Std Dev.	1.581139	1.581139
b	0.8
a	1.6

r	0.8

The formulas are:

Correlation coefficient = zx*zy/n-1 n = 5 in this case

milcah answered 1 year ago

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