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.
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- B
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There appears to be a relationship.

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

(c) Choose the correct graph below.
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- B
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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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