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.
​ $$\begin{array} { | c | c | } \hline \text { No. of units produced } & \text { Cost/unit } \\\hline 20 & 37.7158 \\\hline 35 & 35.0158 \\\hline 50 & 30.8158 \\\hline 65 & 25.8158 \\\hline 80 & 20.0364 \\\hline 95 & 16.9064 \\\hline 110 & 16.3766 \\\hline 120 & 13.8564 \\\hline 135 & 13.9696 \\\hline 150 & 13.847 \\\hline\end{array}$$ ​
​
​
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.

---

Definitions:

Stages

Distinct periods in the development of an individual characterized by specific features, capabilities, or patterns of behavior.

Drawing

The act or skill of producing images on a surface, typically paper, by making marks, usually with a pen, pencil, or crayon.

Male Co-twins

Male siblings that are born during the same pregnancy, sharing a womb simultaneously with their twin.

Testosterone

A steroid hormone produced primarily in the testes in males and the ovaries in females, playing a key role in the development of male reproductive tissues as well as promoting secondary sexual characteristics.