To determine the approximate slope of the line of best fit for the data, we will perform a linear regression analysis. The data provided gives the number of hours of practice and the corresponding number of errors:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|c|}
\hline
\text{Number of hours} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\
\hline
\text{Number of Errors} & 36 & 34 & 30 & 31 & 23 & 16 & 11 & 5 \\
\hline
\end{array}
\][/tex]
From the linear regression analysis, we obtain the following results:
- Slope ([tex]\( m \)[/tex]): [tex]\(-4.55\)[/tex] (approximately),
- Intercept ([tex]\( b \)[/tex]): [tex]\(43.71\)[/tex],
- Correlation coefficient ([tex]\( r \)[/tex]): [tex]\(-0.97\)[/tex],
- P-value: [tex]\(5.42 \times 10^{-5}\)[/tex],
- Standard error ([tex]\( \text{std\_err} \)[/tex]): [tex]\(0.45\)[/tex]
For the slope of the line of best fit, we focus on the slope value, which is approximately [tex]\(-4.55\)[/tex]. This provides the rate at which the number of errors decreases for each additional hour of practice.
Given the following options:
- [tex]$-5.5$[/tex]
- [tex]$-4.5$[/tex]
- [tex]$-2.0$[/tex]
- [tex]$-1.0$[/tex]
The closest slope value to our calculated slope, [tex]\(-4.55\)[/tex], is [tex]\(-4.5\)[/tex].
Thus, the approximate slope of the line of best fit for the data is [tex]\(-4.5\)[/tex].
