$$\text { Find the least-squares line } y = \beta _ { 0 } + \beta _ { z } x \text { that best fits the given data. }$$

question 31

Multiple Choice

$$\text { Find the least-squares line } y = \beta _ { 0 } + \beta _ { z } x \text { that best fits the given data. }$$
-Given: The data points (-2, 2) , (-1, 5) , (0, 5) , (1, 3) , (2, 5) . 44) Suppose the errors in measuring the y-values of the last two data points are greater than for the
Other points. Weight these data points twice as much as the rest of the data. $$\mathrm { X } = \left[ \begin{array} { r r } 1 & - 2 \\1 & - 1 \\1 & 0 \\1 & 1 \\1 & 2\end{array} \right] , \beta = \left[ \begin{array} { l } \beta _ { 1 } \\\beta _ { 2 }\end{array} \right] , \mathrm { y } = \left[ \begin{array} { l } 2 \\5 \\5 \\3 \\5\end{array} \right]$$

• A) \(y = 3.6 + 0.14 x\)
• B) \(y = 7.4 + 0.79 x\)
• C) \(\mathrm { y } = 3.0 + 0.27 \mathrm { x }\)
• D) \(\mathrm { y } = 3.7 + 0.40 \mathrm { x }\)

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Definitions:

Safety Net

Programs or measures designed to provide a minimum level of security, support, or financial assistance to individuals or families, especially in times of unemployment, poverty, or economic hardship.

Sexual Misconduct

Inappropriate behavior of a sexual nature, often involving coercion or abuse of power.

Republican Revolution

A political revolution led by the Republican Party, though the term could refer to different historical events depending on context.

Microprocessor

An integrated circuit that contains the functions of a central processing unit of a computer, responsible for performing arithmetic, logic, controlling, and processing operations.