Question

For a sample of 10 individuals, a researcher calculates residuals for the relationship between “number of delinquent friends” and “number of prior arrests” and finds that the positive residuals = 125. The researcher then collects a second sample of 10 individuals and calculates the residuals on the same two variables and discovers the sum of the positive residuals = 75. What can you conclude about the strength of the relationship between “number of delinquent peers” and “number of prior arrests” across these two random samples? How are they similar/different?

Answer 1

Residuals are the difference between the observed value and the estimated mean response and residual is positive when observed data point lies above the regression line.

Since, size of both sample is equal and based on single residual value, we may not completely describe the relationship. It is know that sum of residuals is zero. If we know the each value of residual for each random sample, then we calculate the standard error to observe the variability of the data.

But we find that form first sample, the distance between observed value and the estimated value is more as compared to second sample residual value. So, strength of the relationship between “number of delinquent peers” and “number of prior arrests” based on sample two may be more because it is near to the estimated regression line value.