A data set is given below.

(a) Draw a scatter diagram. Comment on the type of relation that appears to exist between $x$ and $y$.

(b) Given that $\bar{x} = 3.6667$, $s_x = 2.0656$, $\bar{y} = 4.2333$, $s_y = 1.3794$, and $r = -0.9219$, determine the least-squares regression line.

(c) Graph the least-squares regression line on the scatter diagram drawn in part (a).

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(a) Choose the correct graph below.
- A
- B
- C
- D

There appears to be a relationship.

(b) $\hat{y} = $ (Round to three decimal places as needed.)

(c) Choose the correct graph below.
- A
- B
- C
- D

To answer this question, first plot the data points on a scatter diagram. Then, determine the least-squares regression line equation using the given information. Finally, graph the regression line on the scatter diagram.

Explanation:

(a) To draw a scatter diagram, plot the given data points on a graph, with x-values on the horizontal axis and y-values on the vertical axis. Then, connect the points with a line or curve.

(b) The least-squares regression line equation is y^ = -0.9219x + 8.3289. This equation represents the line that best fits the data points.

(c) To graph the least-squares regression line, plot this equation on the same scatter diagram from part (a) by showing a straight line intercepting the y-axis at 8.3289 and having a slope of -0.9219.

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