Given Below Are Five Observations Collected in a Regression Study $$\begin{array} { l l } \boldsymbol { x } & \boldsymbol { y } \\2 & 4 \\3 & 4 \\4 & 3 \\5 & 2 \\6 & 1\end{array}$$

question 70

Essay

Given below are five observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). $$\begin{array} { l l } \boldsymbol { x } & \boldsymbol { y } \\2 & 4 \\3 & 4 \\4 & 3 \\5 & 2 \\6 & 1\end{array}$$ ​
a.
Develop the least squares estimated regression equation.
b.
At the .05 level of significance, perform a t test and determine whether or not the slope is significantly different from zero.
c.
Perform an F test to determine whether or not the model is significant. Let α = .05.
d.
Compute the coefficient of determination.
e.
Compute the coefficient of correlation.

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Definitions:

Pelvic Girdle

The Pelvic Girdle is a ring-like bony structure, located at the base of the spine, to which the lower limbs are attached in humans and other vertebrates.

Hip Bones

The large bones that form the base of the pelvis and articulate with the femur at the hip joints; these are comprised of three parts: ilium, ischium, and pubis.

Coccyx

The small, triangular bone at the base of the spinal column, consisting of three to five fused vertebrae, also known as the tailbone.

Interosseous Membrane

A fibrous sheet connecting the bones of the forearm (ulna and radius) or the leg (tibia and fibula), providing stability and a surface for muscle attachment.