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d1i1m1o1n [39]
3 years ago
7

If the correlation coefficient in an ordinary least squares regression = 1.00, then A. all the data points must fall exactly on

a straight line with a positive slope. B. all the data points must fall exactly on a straight line with a slope that equals 1.00. C. all the data points must fall exactly on a horizontal straight line with a zero slope. D. all the data points must fall exactly on a straight line with a negative slope.
Mathematics
1 answer:
Hatshy [7]3 years ago
8 0

Answer: Option A is correct.

Step-by-step explanation:

  • The correlation coefficient(r) is a statistical measure that computes the strength of the relationship between two variables.

It lies between -1 and 1.

If the correlation coefficient in an ordinary least squares regression = 1.00.

That indicates that there is a perfect relationship between the variables.

i.e. all the data points must fall exactly on a straight line with a positive slope. .

[when r is positive, the slope of the line is positive].

i.e. option A is correct.

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Fifteen times the square of a non-zero number is equal to 20 times number.What is the number? Its not 4/3
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27% of all college students major in STEM (Science, Technology, Engineering, and Math). If 47 college students are randomly sele
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Answer:

0.12995

0.47508

0.0841

0.738

Step-by-step explanation:

Given that:

Percentage of STEM (p) = 27% = 0.27

Sample size (n) = 47

Using Normal approximation :

Mean (m) = n*p = 47 * 0.27 = 12.69

Standard deviation (s) = √(n*p*q)

q = 1 - p = 1 - 0.27 = 0.73

Standard deviation (s) = √(47*0.27*0.73) = 3.04

a. Exactly 13 of them major in STEM.

P(12.5 < x < 13.5)

USing the z formula :

(x - m) / s

(12.5 - 12.69) / 3.04 < x (13.5 - 12.69) / 3.04

-0.0625 < z < 0.2664

Using the z probability calculator:

P(Z < - 0.0625) = 0.47508

P(Z < 0.2664) = 0.60503

0.60503 - 0.47508

= 0.12995

b. At most 12 of them major in STEM.

P(X ≤ 12.5)

Zscore = (x - m) / s

Zscore = (12.5 - 12.69) / 3.04

Zscore = −0.0625

P(Z ≤ - 0.0625) = 0.47508

c. At least 9 of them major in STEM.

P(X ≥ 8.5)

Zscore = (x - m) / s

Zscore = (8.5 - 12.69) / 3.04

Zscore = −1.378

P(Z ≤ - 1.378) = 0.0841

d. Between 8 and 15 (including 8 and 15) of them major in STEM.

(8.5 - 12.69) / 3.04 < x (15.5 - 12.69) / 3.04

-1.378 ≤ z ≤ 0.924

Using the z probability calculator:

P(Z ≤ 0.924) = 0.82226

P(Z ≤ - 1.378) = 0.084102

0.82226 - 0.084102

= 0.738

5 0
2 years ago
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