1. What is the equation for a regression line? What does each term in the line refer to? 2. What does the standard error of the estimate measure? What is the formula for the standard error of the estimate? 3. For the X,Y data below, compute: a. r and determine if it is significantly different from zero. b. the slope of the regression line and test if it differs significantly from zero. c. the 95% confidence interval for the slope. X Y 4 6 3 7 5 12 11 17 10 9 14 21 4. What assumptions are needed to calculate the various inferential statistics of linear regression? 5. True/false: If the slope of a simple linear regression line is statistically significant, then the correlation will also always be significant. True/false: If the slope of the relationship between X an Y is larger for Population 1 than for Population 2, the correlation will necessarily be larger in Population 1 than in Population 2. Why or why not? True/false: If the correlation is .8, then 40% of the variance is explained. True/false: If the actual Y score was 31, but the predicted score was 28, then the error of prediction is 3. 6. At a school pep rally, a group of sophomore student's organized a free raffle for prizes. They claim they put the names of all the students in the school in the basket and that they randomly drew 36 names out of this basket. Of the prizewinners, 6 were freshmen, 14 were sophomores, 9 were juniors and 7 were seniors. The results do not seem random to you. You think it is a little fishy that sophomores organized the raffle and also won the most prizes. Your school is composed of 30% freshmen, 25% sophomores, 25% juniors and 20% seniors. a. What are the expected frequencies of winners from each class? b. Conduct a significance test to determine whether the winners of the prizes were distributed throughout the classes as would be expected based on the percentage of students in each group. Report your Chi Square and p values. c c. What do you conclude? 8. Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place is shown in Table 11.55. Conduct a test for homogeneity at a 5% level of significance. French Toast Pancake Waffles Omelettes s 47 35 28 53 Women 65 59 55 60 Men 9. According to a flyer by a Prudential Insurance Company representative, the costs of approximate probate fees and taxes for selected net taxable estates are as follows: Net Taxable Estate ($) Approximate Probate Fees and Taxes ($) 600,000 30,000 750,000 92,500 1,000,000 203,000 1,500,000 438,000 2,000,000 688,000 2,500,000 1,037,000 3,000,000 1,350,000 Table 12.32 1. Decide which variable should be the independent variable and which should be the dependent variable. 2. Draw a scatter plot of the data. 3. Does it appear from inspection that there is a relationship between the variables? Why or why not? 4. Calculate the least-squares line. Put the equation in the form of: y = a + bx. 5. Find the correlation coefficient. Is it significant? 6. Find the estimated total cost for a next taxable estate of $1,000,000. Find the cost for $2,500,000. 7. Does it appear that a line is the best way to fit the data? Why or why not? 8. Are there any outliers in the data? 9. Based on these results, what would be the probate fees and taxes for an estate that does not have any assets? 10. What is the slope of the least-squares (best-fit) line? Interpret the slope