$$\text { Find the equation } y = \beta _ { 0 } + \beta _ { 1 } x \text { of the least-squares line that best fits the given data points. }$$

question 43

Multiple Choice

$$\text { Find the equation } y = \beta _ { 0 } + \beta _ { 1 } x \text { of the least-squares line that best fits the given data points. }$$
-Data points: (2, 1) , (3, 2) , (7, 3) , (8, 1) 33) $$\mathrm { X } = \left[ \begin{array} { l l } 1 & 2 \\1 & 3 \\1 & 7 \\1 & 8\end{array} \right] , \mathrm { y } = \left[ \begin{array} { l } 1 \\2 \\3 \\1\end{array} \right]$$

• A) \(y = - \frac { 9 } { 52 } + \frac { 1 } { 13 } x\)
• B) \(y = \frac { 71 } { 52 } - \frac { 1 } { 26 } x\)
• C) \(y = \frac { 71 } { 52 } + \frac { 1 } { 13 } x\)
• D) \(y = - \frac { 105 } { 52 } + \frac { 1 } { 13 } x\)

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Definitions:

Mental Health Facility

An establishment dedicated to the treatment and care of individuals with psychological, behavioral, or cognitive disorders, offering various services and support.

Civil Commitment

Forcing of a person into a mental health facility against his or her will.

Mental Health Professionals

Trained experts who offer services for the evaluation, diagnosis, and treatment of mental health disorders.

Mental Illness

Refers to a wide range of mental health conditions that affect mood, thinking, and behavior.