For the accompanying data set, perform the following tasks:

(a) Draw a scatter diagram of the data.

(b) Compute the correlation coefficient.

(c) Determine whether there is a linear relation between \( x \) and \( y \).

Data:
- \( x: 2, 6, 1, 7, 9 \)
- \( y: 8, 7, 6, 9, 5 \)

To determine whether there's a linear relationship between x and y, create a scatter plot, compute the correlation coefficient (r), and evaluate whether this r value significantly deviates from zero. This process suggests the presence of a linear relationship.

Explanation:

To analyze the relationship between the given x and y variables, we first need to create a scatter plot. Using your x-values as your horizontal axis and y-values as your vertical axis, plot each point. Assess whether or not the points seem to follow a straight line trend; this will visually indicate whether there may be a linear relationship.

Next, we compute the correlation coefficient (r). The correlation coefficient quantifies the strength and direction of the linear relationship between x and y, with a value between -1 and +1. Positive r values indicate a positive correlation, meaning x increases as y increases, and vice versa for a negative correlation. It can be calculated using the formula provided in the reference information.

Finally, if the computed correlation coefficient significantly deviates from zero, that means we have sufficient evidence to conclude there is a significant linear relationship between x and y. We cannot directly determine this without doing the calculations, but that is the methodology you would follow.

Learn more about Correlation Coefficient here:

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For the accompanying data set, perform the following tasks:(a) Draw a scatter diagram of the data.(b) Compute the correlation coefficient.(c) Determine whether there is a linear relation between \( x \) and \( y \).Data:- \( x: 2, 6, 1, 7, 9 \)- \( y: 8, 7, 6, 9, 5 \)

Answer :

Final answer:

Explanation:

Other Questions

For the accompanying data set, perform the following tasks:

(a) Draw a scatter diagram of the data.

(b) Compute the correlation coefficient.

(c) Determine whether there is a linear relation between \( x \) and \( y \).

Data:
- \( x: 2, 6, 1, 7, 9 \)
- \( y: 8, 7, 6, 9, 5 \)