Consider the Following Pairs of Observations $\begin{array}{|l|l|l|l|l|l|}\hline x & 2 & 0 & 3 & 3 & 5 \\\hline y & 1 & 3 & 4 & 6 & 7 \\\hline\end{array}$

question 47

Essay

Consider the following pairs of observations: $\begin{array}{|l|l|l|l|l|l|}\hline x & 2 & 0 & 3 & 3 & 5 \\\hline y & 1 & 3 & 4 & 6 & 7 \\\hline\end{array}$

a. Construct a scattergram for the data.
b. Find the least squares line, and plot it on your scattergram.
c. Find a $99 \%$ confidence interval for the mean value of $y$ when $x = 1$ .
d. Find a $99 \%$ prediction interval for a new value of $y$ when $x = 1$ .

---

Definitions:

Presumed Consent

A legal framework where individuals are assumed to have consented to certain practices (like organ donation) unless they have expressed otherwise.

Altruistic Donation

The act of giving or donating something, such as an organ, without expecting any compensation or benefit in return, motivated solely by the desire to help others.

Social Worth

The perceived value of an individual or group based on societal standards, often influencing access to resources and opportunities.

Social Calculus

A theoretical framework for quantifying the social costs and benefits of individual actions or policies.