(a) Draw a scatter diagram of the data. Choose the correct graph below.

(b) By hand, compute the correlation coefficient. The correlation coefficient is [tex]r=[/tex] (Round to three decimal places as needed.)

(c) Determine whether there is a linear relation between [tex]x[/tex] and [tex]y[/tex].

- Because the correlation coefficient is [blank] and the absolute value of the correlation coefficient is [blank] than the critical value for this data set, [fill in the blank] linear relation exists between [tex]x[/tex] and [tex]y[/tex]. (Round to three decimal places as needed.)

For the accompanying data set, follow these steps:
- (a) Draw a scatter diagram of the data.
- (b) By hand, compute the correlation coefficient.
- (c) Determine whether there is a linear relation between [tex]x[/tex] and [tex]y[/tex].

Click here to view the data set. Click here to view the critical values table.

The question pertains to statistical skills: plotting scatter diagrams, calculating the correlation coefficient, and determining if there's a linear relationship. The correlation coefficient measures the linear relationship between variables. Still, without any provided data, the actual steps can't be shown, only explained.

Explanation:

The subject question relates to the skills of plotting a scatter diagram, calculating the correlation coefficient, and determining linear relationships in mathematics statistics. Unfortunately, without any data provided, we cannot make the calculation, but I can explain the steps.

Step (a) involves plotting data points on a scatter plot graph. This helps us visualize the relationship between the different variables, denoted usually by 'x' and 'y'.

Step (b) deals with the computation of the correlation coefficient, denoted as 'r'. It evaluates the linear relationship between the 'x' and 'y' variables. The value of 'r' lies between -1 to 1. A value close to 1 signifies a strong direct (increase) linear relationship, a value close to -1 signifies a strong inverse (decrease) linear relationship, and a value close to 0 signifies no linear relationship.

Lastly, for step (c), if the absolute value of 'r' is greater than the critical value for the given data set from the critical value table, we can conclude that a linear relation exists, otherwise, it does not.

Learn more about Correlation Coefficient here:

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