Presentation on theme: "1.What is Pearson’s coefficient of correlation? 2.What proportion of the variation in SAT scores is explained by variation in class sizes? 3.What is the."— Presentation transcript:
1.What is Pearson’s coefficient of correlation? 2.What proportion of the variation in SAT scores is explained by variation in class sizes? 3.What is the regression equation? 4.If class size is reduced by an average of one student, what will be the impact on SAT scores? 5.Is there a significant relationship between class size and SAT scores? 6.What test did you perform to answer 5 and what is the p-value of the test? The dependent (y) variable is average SAT score; the independent (x) variable is average class size. Data are for the 50 states and DC.
The independent (x) variable is the percentage of each state’s population who have at least a bachelor’s degree. 1.What proportion of the variation in SAT scores is explained by variation in bachelors’ degrees? 2.What is the standard error of the estimate s y.x ? 3.Predict the average SAT score in a state in which 20% of the population hold bachelors’ degrees. 4.What is the t statistic for the test H 0 : 1 = 0? What is the p-value of the test? 5.At 5% significance should you reject H 0 ? Is there a statistically significant relationship between SAT and Bachelor?
The independent (x) variable is Law Enforcement Officers per 1000 population (LE); the dependent variable is violent crimes per 1000 population (VC). Data are for 97 NC counties. 1.What is the correlation coefficient between LE and VC? 2.What proportion of the variation in crime is explained by variation in the number of law enforcement officers? 3.What is the regression equation? 4.Predict the crime rate for a county that has 5 law enforcement officers per 1000 population. 5.Give a confidence interval for the crime rate in all counties with LE = 5. 6.Give a prediction interval for the crime rate in a county in which LE = 3. 7.Give a 95% confidence interval for the value of 1. 8.Is there a significant relationship between LE and VC? 9.What hypothesis test did you perform to answer question 7? What was the p-value of the test? 10.Would this regression analysis support the theory that counties with higher crime rates tend to hire more law enforcement officers? There are two more slides with this set of questions.
The chart above refers to the regression with law enforcement officers as y and violent crime as x. It is a plot of the residuals against values of the violent crime variable. Does this chart show evidence that any of the regression assumptions are not met? If so, what?
The above chart is a just what its title declares; it refers to the regression of cops on crime. Is there evidence that the residuals may not be normally distributed?