A Regression and Correlation Analysis Resulted in the Following Information

question 26

Essay

A regression and correlation analysis resulted in the following information regarding an independent variable (x) and a dependent variable (y). $$\begin{array} { l l } \sum x = 42 & \sum ( y - y ) ( x - x ) = 37 \\\Sigma y = 63 & \sum ( x - \bar { x } ) ^ { 2 } = 84 \\n = 7 & \Sigma ( y - \bar { y } ) ^ { 2 } = 28 \\& \sum ( y - \widehat { y } ) ^ { 2 } = 11.7024\end{array}$$ ​
a.
Develop the least squares estimated regression equation.
b.
At a .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.

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Definitions:

Neural Cells

Specialized cells in the nervous system that function to process and transmit information through electrical and chemical signals.

Cerebral Cortex

The outer layer of the cerebrum in the brain, involved in complex mental processes such as thought, perception, and decision-making.

Cerebrum

The largest part of the brain, responsible for cognitive functions such as thought, memory, and decision-making.

Motor Cortex

The motor cortex is a region of the brain involved in the planning, control, and execution of voluntary movements.