Question

the accompanying data are the heart rates (in beats per minute) and qt intervals (in milliseconds) for 13 males. the qt interval is a measure of electrical waves of the heart. a lengthened qt interval can indicate heart health problems. find the equation of the regression line. then construct a scatter plot of the data and draw the regression line. then use the regression equation to predict the value of y for each of the given x - values, if meaningful. if the x - value is not meaningful to predict the value of y, explain why not.
(a) ( x = 120 ) bpm
(b) ( x = 68 ) bpm
(c) ( x = 90 ) bpm
(d) ( x = 84 ) bpm
click the icon to view the table of heart rates and qt intervals.
the equation of the regression line is ( hat{y}=-2.09x + 524.59 ).
(round to two decimal places as needed.)
construct a scatter plot of the data and draw the regression line. choose the correct graph below.

Explanation:

The regression equation is given as $\hat{y} = -2.09x + 524.59$, which has a negative slope. We need to check which graph shows a negative linear trend matching this equation.

• Graph A: Positive slope (incorrect, since our slope is negative).
• Graph B: Negative slope, and the line aligns with the scatter points (consistent with the regression equation).
• Graph C: Positive slope (incorrect).
• Graph D: Negative slope but the line does not fit the scatter points as well as Graph B.

Answer:

B. [Graph B]