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Linear Regression t- Procedures

Linear Regression t- Procedures. Just a quick overview. In 2002, there were 23 states in which more than 50% of high school graduates took the SAT test. The following printout gives the regression analysis for predicting SAT Math from SAT Verbal from these 23 states.

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Linear Regression t- Procedures

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  1. Linear Regression t-Procedures Just a quick overview

  2. In 2002, there were 23 states in which more than 50% of high school graduates took the SAT test. The following printout gives the regression analysis for predicting SAT Math from SAT Verbal from these 23 states. • What is the equation of the least-squares regression line for predicting Math SAT score from Verbal SAT score? =185.77 + 0.6419 (Verbal)

  3. In 2002, there were 23 states in which more than 50% of high school graduates took the SAT test. The following printout gives the regression analysis for predicting SAT Math from SAT Verbal from these 23 states. =185.77 + 0.6419 (Verbal) • Interpret the slope of the regression line and interpret in the context of the problem.

  4. In 2002, there were 23 states in which more than 50% of high school graduates took the SAT test. The following printout gives the regression analysis for predicting SAT Math from SAT Verbal from these 23 states. =185.77 + 0.6419 (Verbal) • Identify the standard error of the slope of the regression line and interpret it in the context of the problem.

  5. In 2002, there were 23 states in which more than 50% of high school graduates took the SAT test. The following printout gives the regression analysis for predicting SAT Math from SAT Verbal from these 23 states. =185.77 + 0.6419 (Verbal) • Identify the standard error of the residuals and interpret it in the context of the problem. • The standard error of the residuals is s = 7.457. This value is a measure of variation in SAT Verbal for a fixed value of SAT Math.

  6. In 2002, there were 23 states in which more than 50% of high school graduates took the SAT test. The following printout gives the regression analysis for predicting SAT Math from SAT Verbal from these 23 states. =185.77 + 0.6419 (Verbal) • How did the find the t ratio (aka t-statistic)? • t = • To estimate p-value, use table.

  7. =185.77 + 0.6419 (Verbal) • Construct and interpret a 95% confidence interval for the true slope of the regression line. To get t*, use df = n – 2 (because we have 2 variables). n = 23, so df = 21. Go to 95% confidence in the t-distribution chart.

  8. =185.77 + 0.6419 (Verbal) • Construct and interpret a 95% confidence interval for the true slope of the regression line. We are 95% confident that for each 1 point increase in SAT Verbal, the true increase in the SAT Math score will be between 0.35 and 0.94 points.

  9. The following table gives the number of manatees killed by powerboats along the Florida coast in the years 1977 to 1990, along with the number of powerboat registrations (in thousands) during those years: Enter Data in L1 and L2.

  10. Test the hypothesis that there is a positive linear relationship between the number of powerboat registrations and the number of manatees killed by powerboats. Assume that the conditions needed to do inference for regression have been met. • Let β = the true slope of the regression line for predicting the number of manatees killed by powerboats from the number of powerboat registrations. • H0: β = 0. • HA: β > 0. We use β as the parameter for the slope. b is our sample slope. We use > because they say “positive linear relationship”.

  11. Test the hypothesis that there is a positive linear relationship between the number of powerboat registrations and the number of manatees killed by powerboats. Assume that the conditions needed to do inference for regression have been met. • Let β = the true slope of the regression line for predicting the number of manatees killed by powerboats from the number of powerboat registrations. • H0: β = 0. • HA: β > 0. • We use a t-test for the slope of the regression line. The problem tells us that the conditions necessary to do inference for regression are present.

  12. Test the hypothesis that there is a positive linear relationship between the number of powerboat registrations and the number of manatees killed by powerboats. Assume that the conditions needed to do inference for regression have been met. • Let β = the true slope of the regression line for predicting the number of manatees killed by powerboats from the number of powerboat registrations. • H0: β = 0. • HA: β > 0. • We use a t-test for the slope of the regression line. The problem tells us that the conditions necessary to do inference for regression are present. • Using our calculator: STAT  TESTS  LinRegTTest

  13. Test the hypothesis that there is a positive linear relationship between the number of powerboat registrations and the number of manatees killed by powerboats. Assume that the conditions needed to do inference for regression have been met. • Let β = the true slope of the regression line for predicting the number of manatees killed by powerboats from the number of powerboat registrations. • H0: β = 0. • HA: β > 0. • We use a t-test for the slope of the regression line. The problem tells us that the conditions necessary to do inference for regression are present.

  14. Test the hypothesis that there is a positive linear relationship between the number of powerboat registrations and the number of manatees killed by powerboats. Assume that the conditions needed to do inference for regression have been met. • Let β = the true slope of the regression line for predicting the number of manatees killed by powerboats from the number of powerboat registrations. • H0: β = 0. • HA: β > 0. • We use a t-test for the slope of the regression line. The problem tells us that the conditions necessary to do inference for regression are present. t = 9.675 p-value is essentially 0

  15. Test the hypothesis that there is a positive linear relationship between the number of powerboat registrations and the number of manatees killed by powerboats. Assume that the conditions needed to do inference for regression have been met. • Let β = the true slope of the regression line for predicting the number of manatees killed by powerboats from the number of powerboat registrations. • H0: β = 0. • HA: β > 0. • We use a t-test for the slope of the regression line. The problem tells us that the conditions necessary to do inference for regression are present. t = 9.675 p-value is essentially • Because the P-value is very small, we reject the null. We have very strong evidence of a positive linear relationship between the number of powerboat registrations and the number of manatees killed by powerboats.

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