Question

measurements on young children in mumbai, india, found this least-squares line for predicting height y from arm span x: suppose that a tall child with arm span 120 cm and height 118 cm was added to the sample used in this study. what effect will adding this child have on the correlation and the slope of the least squares regression line?

Answer 1

Adding a tall child with arm span of 120 cm and height of 118 cm to the dataset can affect both correlation and the slope of the least-squares regression line, making the correlation stronger or weaker and changing the slope accordingly.

Step-by-step explanation:

Adding a tall child with an arm span of 120 cm and a height of 118 cm to the sample for predicting height y from arm span x could potentially impact both the correlation and the slope of the least-squares regression line. If the child’s height and arm span are in line with the existing data trend, then the correlation could increase, reflecting a stronger linear relationship. However, if this new point is an outlier and does not fit the existing trend, it could decrease the correlation.

The slope of the regression line is calculated based on the ratio of the covariance of x and y to the variance of x. If the new data point follows the same trend as the other data points (increasing x corresponding to increasing y), the slope could become steeper. Conversely, if the data point significantly deviates from the trend, causing a weaker relationship, the slope might become less steep or even change direction.