Question

5.1

The accompanying data are x = cost (cents per serving) and y = fiber content (grams per serving) for 18 high-fiber cereals rated by a magazine.

Cost per

Serving

Fiber per
Serving

Cost per
Serving

Fiber per
Serving

39 7 53 13  
46 10 53 10  
49 10 67 8  
62 7 43 12  
41 8 48 7  
19 7 28 14  
77 12 54 7  
71 12 27 8  
30 8 57 8  

(a)

Compute the value of the correlation coefficient for this data set. (Round your answer to three decimal places.)

r =  

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b)

The serving size differed for the different cereals, with serving sizes varying from 1/2 cup to 1 1/4 cups. Converting price and fiber content to "per cup" rather than "per serving" results in the accompanying data.

Cost per Cup	Fiber per Cup	Cost per Cup	Fiber per Cup
9.3	44	13	53
10	46	10	53
10	49	8	67
7	62	12	43
6.4	32.8	7	48
7	19	28	56
12	77	7	54
9.6	56.8	16	54
8	30	10.7	71.3

Compute the value of the correlation coefficient for this new data set. (Round your answer to three decimal places.)

r =

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The accompanying data were read from graphs that appeared in an article. The variables shown are the number of acres burned in forest fires in the western United States and timber sales.

Year Number of

Acres Burned

(thousands) Timber Sales

(billions of

board feet)

1945 207 2.1

1950 248 3.8

1955 252 4.5

1960 378 7.0

1965 70 9.6

1970 445 11.0

1975 174 11.1

1980 243 10.1

1985 440 10.2

1990 405 10.9

1995 184 3.8

(a) Compute the correlation coefficient. (Give the answer to three decimal places.)

r =  

Answer 1

solution :

(a) Given data cost x as 39,46,49,62,41,19,77,71,30,53,53,67,43,48,28,54,27,57
fiber y as 7,10,10,7,8,7,12,12,8,13,10,8,12,7,14,7,8,8

=> The corelation coefficient is r = 0.188

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b) Given that cost per cup x as 9.3,10,10,7,6.4,7,12,9.6,8,13,10,8,12,7,28,7,16,10.7
fiber per cup y as 44,46,49,62,32.8,19,77,56.8,30,53,53,67,43,48,56,54,54,71.3

   => The corelation coefficient is r = 0.251

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(a) Given that number of acres x as 207,248,252,378,70,445,174,243,440,405,184
timber sales y as 2.1,3.8,4.5,7.0,9.6,11.0,11.1,10.1,10.2,10.9,3.8

=> The corelation coefficient is r = 0.333