Question

a random sample of 12 casual runners was selected. for each runner, the number of hours they run per week (x) and their resting heart rates in beats per minute (y) were recorded. the scatter - plot displays the resting heart rates versus the number of hours run per week. also shown is the least - squares regression line. y = 80.99+0.12x. point a is an influential point. a new least - squares regression line will be calculated with the influential point removed. how will the removal of the influential point affect the new least - squares regression line for the remaining 11 points? a) the y - intercept will remain the same, and the slope will be negative. b) the y - intercept will decrease, and the slope will be negative. c) the y - intercept will decrease, and the slope will be positive. d) the y - intercept will increase, and the slope will be negative. e) the y - intercept will increase, and the slope will be positive.

Explanation:

Step1: Understand influential points

Influential points can pull the regression line in their direction.

Step2: Analyze the scatter - plot trend

From the scatter - plot, we can see that the overall trend is negative (more hours of running is associated with lower resting heart rates). The influential point is likely pulling the line downwards.

Step3: Consider the effect of removal

When the influential point is removed, the line will shift upwards (increase in y - intercept) and still follow the overall negative trend (negative slope).

Answer:

D. The y - intercept will increase, and the slope will be negative.