Question

It is thought that prehistoric Indians did not take their best tools, pottery, and household items

when they visited higher elevations for their summer camps. It is hypothesized that

archaeological sites tend to lose their cultural identity and specific cultural affiliation as the

elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological

site in the southwestern United States. Let y be the percentage of unidentified artifacts (no

specific cultural affiliation) at a given elevation. Suppose that the following data were obtained

for a collection of archaeological sites in New Mexico:

x

5.50

6.25

6.75

7.25

7.50

y

9

38

38

50

72

What percentage of the variation in y can be explained by the corresponding variation in x and

the least-squares line?

9. Let x be a random variable that represents the percentage of successful free throws a

professional basketball player makes in a season. Let y be a random variable that represents the

percentage of successful field goals a professional basketball player makes in a season. A

random sample of n = 6 professional basketball players gave the following information.

x

87

88

70

84

78

76

y

53

57

50

51

46

50

Given that S

e

? 3.054, a ? 16.547, b ? 0.425, and

, find the predicted percentage

of

successful field goals for a player with x = 73% successful free throws.

Let x be a random variable that represents the percentage of successful free throws a

professional basketball player makes in a season. Let y be a random variable that represents the

percentage of successful field goals a professional basketball player makes in a season. A

random sample of n = 6 professional basketball players gave the following information.

x

64

64

88

66

64

72

y

38

45

50

45

45

41

Given that ?x = 418, ?y = 264, ?x

2

= 29,572, ?y

2

= 11,700, ?xy = 18,514, and r = 0.627, find

the critical value for a test using a 2.5% level of significance claiming that ? is greater than zero.

Answer 1

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	5.5	9	30.25	81	49.5
	6.25	38	39.0625	1444	237.5
	6.75	38	45.5625	1444	256.5
	7.25	50	52.5625	2500	362.5
	7.5	72	56.25	5184	540
Total	33.25	207	223.6875	10653	1446

Sample size: n=

Now,

The coeffcient of correlation is :

The coeffcient of determination is:

That is 89.9% of the variation in y can be explained by the corresponding variation in x.

Slope of the regression equation is

and intercept of the equation will be

So the regression equation will be

y'=-137.9563+26.9709x