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 y represent 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 0.249 0.265 0.286 0.263 0.268 0.339 0.299 y 1.1 3.0 5.5 3.8 3.5 7.3 5.0 (a) Make a scatter diagram of the data. Selection Tool Line Ray Segment Circle Vertical Parabola Horizontal Parabola Point No Solution Help 0.010.020.030.040.050.060.070.080.090.10.110.120.130.140.150.160.170.180.190.20.210.220.230.240.250.260.270.280.290.30.310.320.3312345678 Clear Graph Delete Layer Fill WebAssign Graphing Tool Graph LayersToggle Open/Closed Submission Data Incorrect: Your answer is incorrect. Then visualize the line you think best fits the data. (b) Use a calculator to verify that Σx = 1.969, Σx2 = 0.559, Σy = 29.2, Σy2 = 145.44 and Σxy = 8.549. Compute r. (Round to 3 decimal places.) Incorrect: Your answer is incorrect. As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer.

Answer 1

a) Scatterplot:

b)

X	Y	XY	X²	Y²
0.249	1.1	0.2739	0.062	1.21
0.265	3.0	0.795	0.07023	9
0.286	5.5	1.573	0.0818	30.25
0.263	3.8	0.9994	0.06917	14.44
0.268	3.5	0.938	0.07182	12.25
0.339	7.3	2.4747	0.11492	53.29
0.299	5.0	1.495	0.0894	25
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
1.969	29.2	8.549	0.559337	145.44

Sample size, n =	7
SSxx = Ʃx² - (Ʃx)²/n = 0.55934 - (1.969)²/7 =	0.00548543
SSyy = Ʃy² - (Ʃy)²/n = 145.44 - (29.2)²/7 =	23.6342857
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 8.549 - (1.969)(29.2)/7 =	0.33545714

Ʃ x = 1.969

Ʃ y = 29.2

Ʃ xy = 8.549

Ʃ x² = 0.559337

Ʃ y² = 145.44

Correlation coefficient, r = SSxy/√(SSxx*SSyy)

= 0.33546/√(0.00549*23.63429) = 0.9317 = 0.932

The correlation coefficient is positive.

So, As x increases, the value of r imply that y tend to increase.