Answer :
To find the equation of the line of best fit, we need to determine the slope and y-intercept that best represent the relationship between the given data points.
Given the data points:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 4 & 3 \\ \hline 6 & 4 \\ \hline 8 & 9 \\ \hline 11 & 12 \\ \hline 13 & 17 \\ \hline \end{array} \][/tex]
The line of best fit is given by the equation:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
For this dataset, after performing linear regression analysis, we find that the slope ([tex]\( m \)[/tex]) is 1.560 and the y-intercept ([tex]\( b \)[/tex]) is -4.105.
Thus, the equation of the line of best fit, rounded to three decimal places, is:
[tex]\[ y = 1.560x - 4.105 \][/tex]
Going through the options provided:
[tex]\[ \begin{array}{l} \text{A. } y = 4.105x - 1.560 \\ \text{B. } y = -1.560x + 4.105 \\ \text{C. } y = -4.105x + 1.560 \\ \text{D. } y = 1.560x - 4.105 \\ \end{array} \][/tex]
The correct answer is:
D. [tex]\( y = 1.560x - 4.105 \)[/tex]
Given the data points:
[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 4 & 3 \\ \hline 6 & 4 \\ \hline 8 & 9 \\ \hline 11 & 12 \\ \hline 13 & 17 \\ \hline \end{array} \][/tex]
The line of best fit is given by the equation:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
For this dataset, after performing linear regression analysis, we find that the slope ([tex]\( m \)[/tex]) is 1.560 and the y-intercept ([tex]\( b \)[/tex]) is -4.105.
Thus, the equation of the line of best fit, rounded to three decimal places, is:
[tex]\[ y = 1.560x - 4.105 \][/tex]
Going through the options provided:
[tex]\[ \begin{array}{l} \text{A. } y = 4.105x - 1.560 \\ \text{B. } y = -1.560x + 4.105 \\ \text{C. } y = -4.105x + 1.560 \\ \text{D. } y = 1.560x - 4.105 \\ \end{array} \][/tex]
The correct answer is:
D. [tex]\( y = 1.560x - 4.105 \)[/tex]