Question

Below are four bivariate data sets and the scatter plot for each. (Note that each scatter plot is displayed on the same scale.) Each data set is made up of sample values drawn from a population.

x y 1.0 10.0 2.0 9.0 3.0 8.0 4.0 7.0 5.0 6.0 6.0 5.0 7.0 4.0 8.0 3.0 9.0 2.0 10.0 1.0	x 1 2 3 4 5 6 7 8 9 10 11 y 1 2 3 4 5 6 7 8 9 10 11 0 Figure 1		u v 1.0 7.3 2.0 9.1 3.0 7.2 4.0 5.3 5.0 8.0 6.0 5.2 7.0 4.2 8.0 7.1 9.0 6.2 10.0 3.6	u 1 2 3 4 5 6 7 8 9 10 11 v 1 2 3 4 5 6 7 8 9 10 11 0 Figure 2
w t 1.0 2.5 2.0 4.3 3.0 3.6 4.0 5.3 5.0 4.5 6.0 7.1 7.0 5.9 8.0 7.6 9.0 6.9 10.0 8.1	w 1 2 3 4 5 6 7 8 9 10 11 t 1 2 3 4 5 6 7 8 9 10 11 0 Figure 3		m n 1.0 3.8 2.0 6.7 3.0 8.0 4.0 8.8 5.0 9.6 6.0 9.8 7.0 9.0 8.0 8.0 9.0 6.7 10.0 4.0	m 1 2 3 4 5 6 7 8 9 10 11 n 1 2 3 4 5 6 7 8 9 10 11 0 Figure 4

Answer the following questions. The same response may be the correct answer for more than one question.

1. Which data set indicates the strongest negative linear relationship between its two variables? Choose onethe x, y data setthe u, v data setthe w, t data setthe m, n data set 2. In which data set is there evidence of a strong nonlinear relationship between the two variables? Choose onethe x, y data setthe u, v data setthe w, t data setthe m, n data setnone of the data sets 3. Which data set indicates a perfect positive linear relationship between its two variables? Choose onethe x, y data setthe u, v data setthe w, t data setthe m, n data setnone of the data sets 4. Which data set has an apparent positive, but not perfect, linear relationship between its two variables? Choose onethe x, y data setthe u, v data setthe w, t data setthe m, n data setnone of the data sets

Answer 1

This is a strong negative correlation, which means If X variable increases then Y variable decreases

This is a moderate negative correlation. there is a tendency for U variable increasing with V variable decreasing

3)For w and t

	X	Y	X^2	Y^2	XY
	1	2.5	1	6.25	2.5
	2	4.3	4	18.49	8.6
	3	3.6	9	12.96	10.8
	4	5.3	16	28.09	21.2
	5	4.5	25	20.25	22.5
	6	7.1	36	50.41	42.6
	7	5.9	49	34.81	41.3
	8	7.6	64	57.76	60.8
	9	6.9	81	47.61	62.1
	10	8.1	100	65.61	81
SUM	55	55.8	385	342.24	353.4
n	10
Mean	5.5	5.58
SSxx	82.5	Sum(x^2) - ((Sum(x))^2 /n)	SSR	26.20909	slope * Ssxy	MSR	26.20909
Ssyy	30.876	Sum(y^2) - ((Sum(y))^2 /n)	SSE	4.666909	SST-SSR	MSE	0.583364
Ssxy	46.5	Sum(xy) - (Sum(x)*Sum(y)/n)	SST	30.876	Ssyy
slope	0.563636	Ssxy/SSxx
intercept	2.48	Mean Y - Mean X * Slope
Se	0.763782	SQRT(SSE/(n-2))
Sb1	0.08409	Se/SQRT(SSxx)
r	0.921331	Ssxy/SQRT(SSxx*Ssyy)
r^2	0.84885

This is a strong positive correlation, If w variable increases then t variable increases

4)

	X	Y	X^2	Y^2	XY
	1	3.8	1	14.44	3.8
	2	6.7	4	44.89	13.4
	3	8	9	64	24
	4	8.8	16	77.44	35.2
	5	9.6	25	92.16	48
	6	9.8	36	96.04	58.8
	7	9	49	81	63
	8	8	64	64	64
	9	6.7	81	44.89	60.3
	10	4	100	16	40
SUM	55	74.4	385	594.86	410.5
n	10
Mean	5.5	7.44
SSxx	82.5	Sum(x^2) - ((Sum(x))^2 /n)	SSR	0.020485	slope * Ssxy	MSR	0.020485
Ssyy	41.324	Sum(y^2) - ((Sum(y))^2 /n)	SSE	41.30352	SST-SSR	MSE	5.162939
Ssxy	1.3	Sum(xy) - (Sum(x)*Sum(y)/n)	SST	41.324	Ssyy
slope	0.015758	Ssxy/SSxx
intercept	7.353333	Mean Y - Mean X * Slope
Se	2.27221	SQRT(SSE/(n-2))
Sb1	0.250162	Se/SQRT(SSxx)
r	0.022265	Ssxy/SQRT(SSxx*Ssyy)
r^2	0.000496

technically a positive correlation, the relationship between m and n variables is weak