To determine which scatterplot has a trend line with a positive slope, we need to evaluate the data from both scatterplots and understand the slope of the trend line (often referred to as the line of best fit) for each dataset.
Firstly, here are the datasets provided:
Scatterplot 1:
[tex]\[
\begin{tabular}{c|c}
$x_1$ & $y_1$ \\
\hline
1 & 4.5 \\
1.5 & 5.5 \\
2 & 4.25 \\
2.5 & 5 \\
3 & 3.75 \\
3.5 & 3.5 \\
3.5 & 4.25 \\
\end{tabular}
\][/tex]
Scatterplot 2:
[tex]\[
\begin{tabular}{c|c}
$x_1$ & $y_1$ \\
\hline
1 & 25 \\
1.5 & 3.5 \\
2 & 1.25 \\
2.5 & 0.25 \\
3 & 3 \\
3.5 & 1.5 \\
3.5 & 1.75 \\
\end{tabular}
\][/tex]
Step-by-Step Solution:
1. Calculating the Slope for Scatterplot 1:
- The data points are: [tex]\( (1, 4.5), (1.5, 5.5), (2, 4.25), (2.5, 5), (3, 3.75), (3.5, 3.5), (3.5, 4.25) \)[/tex].
- Using linear regression, we can calculate the slope of the trend line for these data points.
- The slope for Scatterplot 1 is [tex]\(-0.446875\)[/tex].
2. Calculating the Slope for Scatterplot 2:
- The data points are: [tex]\( (1, 25), (1.5, 3.5), (2, 1.25), (2.5, 0.25), (3, 3), (3.5, 1.5), (3.5, 1.75) \)[/tex].
- Using linear regression, we can calculate the slope of the trend line for these data points.
- The slope for Scatterplot 2 is [tex]\(-6.000\)[/tex].
Conclusion:
- Both slopes for Scatterplot 1 and Scatterplot 2 are negative.
- Hence, neither of the provided scatterplots has a trend line with a positive slope.
