Question

(The use of a calculator is easier and likely to minimize mistakes. If you are using a calculator, you can show your work by writing down all the values on the calculator screen, and then circling or writing down the value required.)

15. The number of passes completed against the number of attempts by 9 high school quarterbacks.

Attempt | 5 | 12 | 10 | 14 | 28 | 6 | 15 | 21 | 27

Comp. | 10 | 17 | 14 | 34 | 38 | 10 | 28 | 32 | 47

a. Compute the linear correlation coefficient.

b. What is the nature of the relationship between the variables? (For example: strong and positive.)

16. International weather forecast for selected cities on October 10, 2010, by the Timesfreepress.com in degrees Fahrenheit is given below.

Low | 65 | 40 | 41 | 54 | 73 | 53 | 79 | 59 | 45

High | 76 | 64 | 52 | 66 | 94 | 70 | 88 | 83 | 56

a. Compute the linear correlation coefficient.

b. What is the nature of the relationship between the variables? (For example: strong and positive.)

17. The number of races and the number of wins that the ten top point getters have in the Sprint Cup at Texas is given in Table 4.13. You want to find out if the number of wins depends on the number of races.

# races | 14 | 10 | 15 | 19 | 11 | 11 | 17 | 16 | 15 | 19

# wins | 1 | 1 | 0 | 1 | 0 | 3 | 1 | 1 | 1 | 2

a. Independent variable: ___________________ Dependent variable: ___________________

b. Compute the linear correlation coefficient.

c. What proportion of the dependent variable is determined by the variation in the independent variable and what proportion is not? Show your work.

18. Table 4.14 gives the number of races and the average finish by the ten top point getters in a racing competition. You want to find out if the average finish depends on the number of races.

# races | 14 | 10 | 15 | 19 | 11 | 11 | 17 | 16 | 15 | 19

average finish | 3 | 4 | 2 | 1 | 4 | 3 | 5 | 1 | 3 | 4

a. Independent variable: ___________________ Dependent variable: ___________________

b Compute the linear correlation coefficient.

c. What proportion of the dependent variable is determined by the variation in the independent variable and what proportion is not? Show your work.

Answer 1

Question 15

	Attempt ( X )	Comp. ( Y )	X * Y	X2	Y2
	5	10	50	25	100
	12	17	204	144	289
	10	14	140	100	196
	14	34	476	196	1156
	28	38	1064	784	1444
	6	10	60	36	100
	15	28	420	225	784
	21	32	672	441	1024
	27	47	1269	729	2209
Total	138	230	4355	2680	7302

Part b)

Since the value of r = 0.9242 closer to 1 and positive, we can say that there is positive strong correlation between the two variables.

Question 16

	Low ( X )	High ( Y )	X * Y	X2	Y2
	65	76	4940	4225	5776
	40	64	2560	1600	4096
	41	52	2132	1681	2704
	54	66	3564	2916	4356
	73	94	6862	5329	8836
	53	70	3710	2809	4900
	79	88	6952	6241	7744
	59	83	4897	3481	6889
	45	56	2520	2025	3136
Total	509	649	38137	30307	48437

Part b)

There is strong positive correlation between the two variables.