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Find the linear function that is the best fit for the data.

[tex]\[
\begin{tabular}{|c|c|c|c|c|c|}
\hline
$x$ & 1 & 3 & 5 & 7 & 9 \\
\hline
$y$ & 2 & 3 & 4 & 5 & 6 \\
\hline
\end{tabular}
\][/tex]

What is the linear function of the data?

[tex]\[
y = \square x + (\square)
\][/tex]

(Type integers or decimals.)

Sagot :

GinnyAnswer
To find the linear function that best fits the given data points, we'll use the method of linear regression to determine the slope (m) and the intercept (b) of the line [tex]\( y = mx + b \)[/tex].

We are given the following data points:

[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 3 & 5 & 7 & 9 \\ \hline y & 2 & 3 & 4 & 5 & 6 \\ \hline \end{array} \][/tex]

Using linear regression, the best fit line through these points is determined by calculating the slope (m) and the y-intercept (b) such that [tex]\( y = mx + b \)[/tex].

For the given data:
- The slope [tex]\( m \approx 0.5 \)[/tex]
- The intercept [tex]\( b \approx 1.5 \)[/tex]

Therefore, the linear function that best fits the data is:

[tex]\[ y = 0.5x + 1.5 \][/tex]

This is the equation of the linear fit to the given data points.
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