Question

Calculate and record the regression equation. Write a paragraph discussing the slope of the regression equation and how it relates to your topic. Use the following data points.

Height (in.)	Foot Length (in.)
63	10
66	12
62.5	9.4
74	10.5
70	11.3
72	11.3
71	12.5
64	9.1
72	10.9
71	10
74	12.1
67	10
69	11.1
65	9.6
62.8	9
72	11.3
68.8	10.5
69	10
65.3	9
53	7
71	10.3
74	11.7
70	10
72	10.6
72.5	12.8
67	9.5
69	10.9
74	11.6
68	9
70.1	10.1
62	8
77	11.4
63	9.5
64.5	9.4
71	9.8

Answer 1

X-Mx	Y-My	(X-Mx)^2	(X-Mx)(Y-MY)
-5.471	-0.32	29.937	1.751
-2.471	1.68	6.108	-4.152
-5.971	-0.92	35.658	5.494
5.529	0.18	30.565	0.995
1.529	0.98	2.337	1.498
3.529	0.98	12.451	3.458
2.529	2.18	6.394	5.512
-4.471	-1.22	19.994	5.455
3.529	0.58	12.451	2.047
2.529	-0.32	6.394	-0.809
5.529	1.78	30.565	9.841
-1.471	-0.32	2.165	0.471
0.529	0.78	0.279	0.412
-3.471	-0.72	12.051	2.499
-5.671	-1.32	32.165	7.486
3.529	0.98	12.451	3.458
0.329	0.18	0.108	0.059
0.529	-0.32	0.279	-0.169
-3.171	-1.32	10.058	4.186
-15.471	-3.32	239.365	51.365
2.529	-0.02	6.394	-0.051
5.529	1.38	30.565	7.629
1.529	-0.32	2.337	-0.489
3.529	0.28	12.451	0.988
4.029	2.48	16.229	9.991
-1.471	-0.82	2.165	1.207
0.529	0.58	0.279	0.307
5.529	1.28	30.565	7.077
-0.471	-1.32	0.222	0.622
1.629	-0.22	2.652	-0.358
-6.471	-2.32	41.879	15.014
8.529	1.08	72.737	9.211
-5.471	-0.82	29.937	4.487
-3.971	-0.92	15.772	3.654
2.529	-0.52	6.394	-1.315
Mx: 68.471	My: 10.320	Sum: 772.351	Sum: 158.830

Sum of X = 2396.5
Sum of Y = 361.2
Mean X = 68.4714
Mean Y = 10.32
Sum of squares (SS_X) = 772.3514
Sum of products (SP) = 158.83

Regression Equation = ŷ = bX + a

b = SP/SS_X = 158.83/772.35 = 0.2056

a = M_Y - bM_X = 10.32 - (0.21*68.47) = -3.7608

ŷ = 0.2056X - 3.7608

The slope of a regression line (b) represents the rate of change in y as x changes. Because y is dependent on x, the slope describes the predicted values of y given x.

For this case for every increase in x, y will increase by 0.2056