# 3 Regression and Testing Questions

Question One. A researcher is interested in determining the effect of after-school programs on adolescent delinquency. He asks a small sample of students how many activities they participate in and he asks how many delinquent acts they have committed since the school year has begun. His data are below. Calculate the linear regression equation. What is the predicted value of delinquent acts for a student that participated in three after-school activities?

(see attached for tables)

Question Two. A researcher is interested in the effect of school activities on delinquency; however, she thinks that the more years a student has been in school, the more activities the student will be involved in. Consequently, she first decides to analyze the effect of age on delinquency with a small sample from the local school. Her data are below. Calculate the regression equation. Assuming a normal distribution, is the obtained b significant at the alpha 0.05, two-tailed? How many delinquent acts would she predict for a student who is fifteen and a half? How many delinquent acts would she predict for a student who is nine-years-old? How many delinquent acts would she predict for a student who is 25-years-old? Why are the latter two estimates unreliable?

(see attached for tables)

Question Three. A researcher has studied the relationship between socioeconomic status (SES) and delinquency and age and delinquency. However, now she is interested in studying the relationship between age and socioeconomic status. Both variables have been shown to have a negative relationship with delinquency, but this researcher is interested in finding out more about the relationship between age and SES. She has a set of data in which SES is measured in which a low number indicates low SES. The scores on this measure can range from 0-20. Use the sample of data below to draw a scatterplot, calculate the regression equation, and determine . Is the calculated value significant? Test this using an alpha of 0.01.

(see attached for tables)

#### Solution Summary

Solution attaches a .doc file to show how to calculate these 3 statistics questions including scatterplots, hypothesis testing, etc.