Answered

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A calculator was used to perform a linear regression on the values in the table. The results are shown to the right of the table.

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

[tex]\[
\begin{array}{l}
\text{LinReg} \\
y = ax + b \\
a = -3.6 \\
b = 12.8 \\
r^2 = 0.9969 \\
r = -0.9985
\end{array}
\][/tex]

What is the line of best fit?

A. [tex]\( y = 12.8x - 3.6 \)[/tex]
B. [tex]\( y = -3.6x + 12.8 \)[/tex]
C. [tex]\( y = -0.998x + 12.8 \)[/tex]
D. [tex]\( -0.998 = -3.6x + 12.8 \)[/tex]

Sagot :

GinnyAnswer
To determine the line of best fit from the results provided by the linear regression, we need to understand the following equation format for a linear relationship:

[tex]\[ y = ax + b \][/tex]

Where:
- [tex]\( a \)[/tex] is the slope of the line.
- [tex]\( b \)[/tex] is the y-intercept.

Given the results from the linear regression:
- [tex]\( a = -3.6 \)[/tex]
- [tex]\( b = 12.8 \)[/tex]

We can plug these values into the linear equation format to get the line of best fit:

[tex]\[ y = -3.6x + 12.8 \][/tex]

Now, let's compare this line of best fit with the options provided:

A. [tex]\( y = 12.8x - 3.6 \)[/tex]

This option is not correct because it incorrectly switches the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex].

B. [tex]\( y = -3.6x + 12.8 \)[/tex]

This option is correct as it matches our calculated line of best fit.

C. [tex]\( y = -0.998x + 12.8 \)[/tex]

This option is not correct because it has the incorrect slope ([tex]\( a \)[/tex]) value.

D. [tex]\( -0.998 = -3.6x + 12.8 \)[/tex]

This option is not correctly formatted as an equation of a line in the [tex]\( y = ax + b \)[/tex] form.

Therefore, the correct option is:

B. [tex]\( y = -3.6x + 12.8 \)[/tex]
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