Find the linear function that is the best fit for the given data. Round decimal values to the nearest hundredth, if
necessary.
-$\begin{array}{l|ccccc}
x & 2 & 3 & 7 & 8 & 10 \
\hline \mathrm{y} & 3 & 4 & 4 & 5 & 6
\end{array}$

A) $y = 0.30 x + 4.29$
B) $y = 0.30 x + 2.57$
C) $y = 0.32 x + 4.29$
D) $y = 0.32 x + 2.57$

Question

Find the linear function that is the best fit for the given data. Round decimal values to the nearest hundredth, if
necessary.
-$\begin{array}{l|ccccc}
x & 2 & 3 & 7 & 8 & 10 \
\hline \mathrm{y} & 3 & 4 & 4 & 5 & 6
\end{array}$

A) $y = 0.30 x + 4.29$
B) $y = 0.30 x + 2.57$
C) $y = 0.32 x + 4.29$
D) $y = 0.32 x + 2.57$

Quizplus · Accepted Answer

The best fit line can be found using the least squares method, which minimizes the sum of the squares of the vertical distances of the points from the line. The slope (m) of the best fit line can be calculated using the formula $m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}$, and the y-intercept (b) can be calculated using $b = \frac{\sum y - m(\sum x)}{n}$, where n is the number of data points. Plugging in the given values, we find that the slope $m \approx 0.30$ and the y-intercept $b \approx 2.57$, which matches option B.

Find the Linear Function That Is the Best Fit for the Given