Campus crime rates are generally lower than the national average;however thousands of crimes take place on college campuses daily.Cities that are notoriously dangerous would likely be undesirable locations for a college campus.A study examined the crime rates on campuses throughout the United States and whether or not they were significantly affected by surrounding cities.A regression analysis was performed to investigate which characteristics of a city,along with a few chosen demographics of a school,impacted the crime rate on a college campus.There are over 4000 colleges and universities in the United States.The study included a random sample of 129 institutions.The response variable was the number of crimes per 1000 people.Explanatory variables included the percent of married couples in the city (married),tuition of the university (tuition),average income of the city (income),unemployment rate of the city (unemployment),percent of students who belong to a fraternity or sorority (Greek),average age of the students at the university (age),and number of liquor stores in the city (liquor).A complete analysis of the data is shown below. Does the significance test for the individual regression coefficients for marriage and income contradict the information we obtained from the correlation table?
A)Yes,both marriage and income are correlated with crime and the correlation is statistically significant.Therefore,something is wrong with the regression analysis.
B)No,marriage and income are both highly correlated with each other.Therefore,there is likely a significant overlap of the predictive information from these variables.

Question

Campus crime rates are generally lower than the national average;however thousands of crimes take place on college campuses daily.Cities that are notoriously dangerous would likely be undesirable locations for a college campus.A study examined the crime rates on campuses throughout the United States and whether or not they were significantly affected by surrounding cities.A regression analysis was performed to investigate which characteristics of a city,along with a few chosen demographics of a school,impacted the crime rate on a college campus.There are over 4000 colleges and universities in the United States.The study included a random sample of 129 institutions.The response variable was the number of crimes per 1000 people.Explanatory variables included the percent of married couples in the city (married),tuition of the university (tuition),average income of the city (income),unemployment rate of the city (unemployment),percent of students who belong to a fraternity or sorority (Greek),average age of the students at the university (age),and number of liquor stores in the city (liquor).A complete analysis of the data is shown below.       Does the significance test for the individual regression coefficients for marriage and income contradict the information we obtained from the correlation table?
A)Yes,both marriage and income are correlated with crime and the correlation is statistically significant.Therefore,something is wrong with the regression analysis. 
B)No,marriage and income are both highly correlated with each other.Therefore,there is likely a significant overlap of the predictive information from these variables.

Quizplus · Accepted Answer

The correlation table shows that both marriage and income are highly correlated with crime. The individual regression coefficients for marriage and income are also significant in the regression analysis. This does not contradict the information from the correlation table because the high correlation between marriage and income means that there is likely a significant overlap in the predictive information from these variables. Therefore, it is reasonable to see significant coefficients for both variables in the regression analysis.

Campus Crime Rates Are Generally Lower Than the National Average;however