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

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...

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...

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...

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 xbe the elevation (in thousands of feet)
for an archaeological site in the southwestern United States. Let
ybe the percentage of unidentified artifacts (no specific
cultural affiliation) at a given elevation....

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