A Production Company Is Studying the Relationship Between the Average

question 45

Essay

A production company is studying the relationship between the average cost/unit and number of units produced in a batch. A sample of 10 batches is selected and the data is given below.
​ $$\begin{array} { | c | c | } \hline \text { No. of units produced } & \text { Cost/unit } \\\hline 20 & 37.7158 \\\hline 35 & 35.0158 \\\hline 50 & 30.8158 \\\hline 65 & 25.8158 \\\hline 80 & 20.0364 \\\hline 95 & 16.9064 \\\hline 110 & 16.3766 \\\hline 120 & 13.8564 \\\hline 135 & 13.9696 \\\hline 150 & 13.847 \\\hline\end{array}$$ ​
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a. Develop an estimated quadratic regression equation for the data. How much variation in the sample values of cost/unit does this regression model explain?
b. Is the overall regression relationship significant at a 0.05 level of significance? If so, then test the relationship between the independent variable and the dependent variable at a 0.05 level of significance.

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Definitions:

Gastric Glands

Glands located in the lining of the stomach that produce gastric juice, including hydrochloric acid and digestive enzymes.

Gastric Pits

Small depressions in the lining of the stomach where gastric glands open, leading to the production of gastric juice.

Cholecystokinin

Hormone liberated by the upper intestinal mucosa on contact with gastric contents; stimulates the contraction of the gallbladder and the secretion of pancreatic juice high in digestive enzymes.

Pancreatic Bicarbonate

A bicarbonate ion produced by the pancreas that neutralizes stomach acid as it enters the small intestine.