Questions: Shown below are the scatter plots for four different data sets. Answer the questions that follow. The same response may be the correct answer for more than one question. Figure 1 Figure 2 Figure 3 Figure 4 1. Which data set shows the least evidence of a linear relationship? Choose one 2. For which data set is the correlation coefficient r closest to 1? Choose one 3. For which data set does the correlation coefficient r appear to be equal to -1? Choose one

Shown below are the scatter plots for four different data sets.
Answer the questions that follow. The same response may be the correct answer for more than one question.

Figure 1
Figure 2
Figure 3
Figure 4

1. Which data set shows the least evidence of a linear relationship? Choose one

2. For which data set is the correlation coefficient r closest to 1? Choose one

3. For which data set does the correlation coefficient r appear to be equal to -1? Choose one

Transcript text: Shown below are the scatter plots for four different data sets. Answer the questions that follow. The same response may be the correct answer for more than one question. Figure 1 Figure 2 Figure 3 Figure 4 \begin{tabular}{|l|l|} \hline \begin{tabular}{l} 1. Which data set shows the least evidence of a linear \\ relationship? \end{tabular} & Choose one \\ \hline \begin{tabular}{l} 2. For which data set is the correlation coefficient $r$ closest \\ to 1 ? \end{tabular} & Choose one \\ \hline \begin{tabular}{l} 3. For which data set does the correlation coefficient $r$ \\ appear to be equal to -1 ? \end{tabular} & Choose one \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Identify the data set with the least evidence of a linear relationship

Observation: Figure 1 shows a scattered pattern with no clear linear trend.
Conclusion: The data set in Figure 1 shows the least evidence of a linear relationship.

Step 2: Identify the data set with the correlation coefficient $ r $ closest to 1

Observation: Figure 2 shows a strong positive linear relationship.
Conclusion: The data set in Figure 2 has the correlation coefficient $ r $ closest to 1.

Step 3: Identify the data set with the correlation coefficient $ r $ closest to -1

Observation: Figure 4 shows a strong negative linear relationship.
Conclusion: The data set in Figure 4 has the correlation coefficient $ r $ closest to -1.