The regression equation is Ŷ = 30 + 2.56X, the sample size is 14, and the standard error of the slope is 0.97. What is the critical value to test the significance of the slope at the 0.05 significance level?

t = ±2.179

Step-by-step explanation:

Given:

Regression equation = Y = 30 + 2.56X

Sample size, n = 14

Standard error, e = 0.97

Significance level, = 0.05

Required:

Find the critical value

At level of significance = 0.05

Degrees of freedom, df = n - 2 = 14 - 2= 12

Find critical value:

Using t table, two tailed, df = 12, we have:

Therefore, the critical value,

t-critical = ±2.179

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!

-6 is the correct option from the above given options