Question

copy and complete the table and formulas regarding positivity (x) and relational satisfaction (y), below, to answer questions 17 through 23. (round off to two decimal places after each operation.) correlation table

x	y	(x - x̄)	(y - ȳ)	(x - x̄)(y - ȳ)	(x - x̄)²	(y - ȳ)²
4	20
5	23
5	25
7	24
9	28
x̄ =	ȳ =		σ =	σ =	σ =

correlation and linear regression formulas
correlation: r = \frac{\sum((x - x̄)(y - ȳ))}{\sqrt{\sum(x - x̄)²×\sum(y - ȳ)²}}
linear regression: b = r\frac{s_y}{s_x}
s_y = \sqrt{\frac{\sum(y - ȳ)²}{(n - 1)}}
a = ȳ - bx̄
s_x = \sqrt{\frac{\sum(x - x̄)²}{(n - 1)}}
y = a + bx
what is the standard deviation for positivity (x)?

Explanation:

Step1: Calculate the mean of \(x\) values

\(\bar{x}=\frac{4 + 5+5+7+9}{5}=\frac{30}{5}=6\)

Step2: Calculate \((x - \bar{x})\) for each \(x\) value

For \(x = 4\): \(4-6=- 2\); for \(x = 5\): \(5 - 6=-1\); for \(x = 5\): \(5 - 6=-1\); for \(x = 7\): \(7 - 6 = 1\); for \(x = 9\): \(9 - 6=3\)

Step3: Calculate \((x - \bar{x})^2\) for each \(x\) value

\((4 - 6)^2=(-2)^2 = 4\); \((5 - 6)^2=(-1)^2 = 1\); \((5 - 6)^2=(-1)^2 = 1\); \((7 - 6)^2=1^2 = 1\); \((9 - 6)^2=3^2 = 9\)

Step4: Calculate \(\sum(x - \bar{x})^2\)

\(\sum(x - \bar{x})^2=4 + 1+1+1+9=16\)

Step5: Calculate the standard - deviation \(s_x\)

\(s_x=\sqrt{\frac{\sum(x - \bar{x})^2}{n - 1}}\), where \(n = 5\)
\(s_x=\sqrt{\frac{16}{4}}=\sqrt{4}=2.00\)

Answer:

\(2.00\)