Question

In baseball, is there a linear correlation between batting average and home run percentage? Let x represent the batting average of a professional baseball player, and let yrepresent the player's home run percentage (number of home runs per 100 times at bat). A random sample of n = 7 professional baseball players gave the following information.

x	0.253	0.247	0.286	0.263	0.268	0.339	0.299
y	1.1	3.9	5.5	3.8	3.5	7.3	5.0

a) Use a calculator to verify that Σx = 1.955, Σx2 = 0.552, Σy = 30.1, Σy2 = 151.65 and Σxy = 8.722. Compute r. (Round your answer to three decimal places.)____________

Do larger universities tend to have more property crime? University crime statistics are affected by a variety of factors. The surrounding community, accessibility given to outside visitors, and many other factors influence crime rate. Let x be a variable that represents student enrollment (in thousands) on a university campus, and let y be a variable that represents the number of burglaries in a year on the university campus. A random sample of n = 8 universities in California gave the following information about enrollments and annual burglary incidents.

x	13.1	29.6	24.5	14.3	7.5	27.7	16.2	20.1
y	25	77	39	23	15	30	15	25

b) Use a calculator to verify that Σx = 153.0, Σx2 = 3342.50, Σy = 249, Σy2 = 10579 and Σxy = 5580.1. Compute r. (Round to 3 decimal places.)______________

Is the magnitude of an earthquake related to the depth below the surface at which the quake occurs? Let x be the magnitude of an earthquake (on the Richter scale), and let ybe the depth (in kilometers) of the quake below the surface at the epicenter.

x	2.5	4.4	3.3	4.5	2.6	3.2	3.4
y	4.9	10.2	11.2	10.0	7.9	3.9	5.5

(c) Use a calculator to verify that Σx = 23.9, Σx2 = 85.31, Σy = 53.6, Σy2 = 461.36 and Σxy = 190.81. Compute r. (Round to 3 decimal places.)______________

Answer 1

a)

X	Y	XY	X²	Y²
0.253	1.1	0.2783	0.064009	1.21
0.247	3.9	0.9633	0.061009	15.21
0.286	5.5	1.573	0.081796	30.25
0.263	3.8	0.9994	0.069169	14.44
0.268	3.5	0.938	0.071824	12.25
0.339	7.3	2.4747	0.114921	53.29
0.299	5	1.495	0.089401	25

	X	Y	XY	X²	Y²
total sum	1.955	30.1	8.722	0.552	151.65
mean	0.2793	4.3000

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.854
.............

b)

X	Y	XY	X²	Y²
13.1	25	327.5	171.61	625
29.6	77	2279.2	876.16	5929
24.5	39	955.5	600.25	1521
14.3	23	328.9	204.49	529
7.52	15	112.8	56.5504	225
27.7	30	831	767.29	900
16.2	15	243	262.44	225
20.1	25	502.5	404.01	625

	X	Y	XY	X²	Y²
total sum	153.02	249	5580.400	3342.800	10579
mean	19.1275	31.1250

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.754
.....

c)

X	Y	XY	X²	Y²
2.5	4.9	12.25	6.25	24.01
4.4	10.2	44.88	19.36	104.04
3.3	11.2	36.96	10.89	125.44
4.5	10	45	20.25	100
2.6	7.9	20.54	6.76	62.41
3.2	3.9	12.48	10.24	15.21
3.4	5.5	18.7	11.56	30.25

	X	Y	XY	X²	Y²
total sum	23.9	53.6	190.810	85.310	461.36
mean	3.4143	7.6571

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.568
      
.............

done all

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