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 0.243 0.265 0.286 0.263 0.268 0.339 0.299 y 1.1 3.5 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 After you add an object to the graph you can use Graph Layers to view and edit its properties. (b) Use a calculator to verify that Σx = 1.963, Σx2 = 0.556, Σy = 29.7, Σy2 = 148.69 and Σxy = 8.675. Compute r. (Round your answer to three decimal places.) As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer. Given our value of r, y should tend to decrease as x increases. Given our value of r, y should tend to remain constant as x increases. Given our value of r, we can not draw any conclusions for the behavior of y as x increases. Given our value of r, y should tend to increase as x increases.

Answer 1

Part a)

Part b)

	X	Y	X * Y	X2	Y2
	0.243	1.1	0.2673	0.059049	1.21
	0.265	3.5	0.9275	0.070225	12.25
	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
Total	1.963	29.7	8.6749	0.556385	148.69

r = 0.946

Given our value of r, y should tend to increase as x increases.