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:

Bronchioles

Small branches of the bronchi found in the respiratory system that lead air into the alveoli of the lungs.

Digestive System

The digestive system is a group of organs working together to convert food into energy and basic nutrients to feed the entire body.

Teeth

Hard, calcified structures in the mouths of many organisms that are primarily used for biting and chewing food.

Peristalsis

Contractions that propel food through the digestive tract.