What is Pearson

1

1. What is Pearsons 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.
2

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 sy.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 H0 ?1 0?
   What is the p-value of the test?
5. At 5 significance should you reject H0? Is
   there a statistically significant relationship
   between SAT and Bachelor?

The independent (x) variable is the percentage of
each states population who have at least a
bachelors degree.
3
The independent (x) variable is Law Enforcement
Officers per 1000 population (LO) the dependent
variable is violent crimes per 1000 population
(VC). Data are for 97 NC counties.

• What is the correlation coefficient between LO
  and VC?
• What proportion of the variation in crime is
  explained by variation in the number of law
  enforcement officers?
• What is the regression equation?
• Predict the crime rate for a county that has 5
  law enforcement officers per 1000 population.
• Give a 95 confidence interval for the crime rate
  in all counties with LO 5. Assume ?x 2.7 and
  that t95 2.
• Give a 95 prediction interval for the crime rate
  in a county in which LO 3 using the same
  assumed values as in q. 5.
• Give a 95 confidence interval for the value of
  ?1.
• Is there a significant relationship between LO
  and VC?
• What hypothesis test did you perform to answer
  question 7? What was the p-value of the test?
• Would this regression analysis support the theory
  that law enforcement officers tend to cause
  crime?