#2) 12.50 points A recent article in Bloomberg Businessweek listed the \"Best Small Companies.\" We are interested in the current results of the companies' sales and earnings. A random sample of 12 companies was selected and the sales and earnings, in millions of dollars, are reported below. Company Sales ($ millions) Earnings ($ millions) Company ($ millions) Earnings Sales ($ millions) Papa John's International $ 17.5 $ $ Applied Innovation 18.6 87.4 2.6 $ 4.4 4.9 Checkmate Electronics Royal Grip 9.8 1.7 Integracare 17.4 1.3 M-Wave 19.6 71.7 8.0 Serving-N-Slide 53.7 3.5 Wall Data 8.2 Davidson & Associates 6.0 Chico's FAS 58.6 47.3 6.6 4.1 Daig Cobra Golf 28.6 69.2 12.8 Let sales be the independent variable and earnings be the dependent variable. (Round your answers to 3 decimal places.) a. . The coefficient of correlation is b. The coefficient of determination is . c. The regression equation, with the coefficients, is Y' = + X d. For a small company with $54 million in sales, an estimate of the earnings is ($ millions). #3 A suburban hotel derives its revenue from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied. Day 1 Income Occupied $ 31 2 Day Income Occupied 1,452 60 14 $ 1,425 1,361 20 15 1,445 1,426 21 16 1,439 1,470 80 17 1,348 1,456 70 18 1,450 51 3 62 4 45 5 41 6 1,430 29 19 1,431 1,354 30 20 1,446 1,442 21 21 1,485 1,394 15 22 1,405 1,459 36 23 1,461 1,399 41 24 1,490 1,458 35 25 1,426 1,537 51 62 7 47 8 43 9 38 10 36 11 30 12 65 13 PictureClick here for the Excel Data File Use a statistical software package to answer the following questions. b. Determine the coefficient of correlation between the two variables. (Round your answer to 3 decimal places.) Pearson correlation State the decision rule for 0.005 significance level: H0: 0; H1: > 0 (Round your answer to 3 decimal places.) Reject H0 if t > Compute the value of the test statistic. (Round your answer to 2 decimal places.) Value of the test statistic c. Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the 0.005 significance level. H0, There is a between revenue and occupied rooms. d. What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied? (Round your answer to 1 decimal place.) % of the variation in revenue is explained by variation in occupied rooms. #4 Given the following ANOVA table: SourceDF SS MS Regression 1 1,800 1,800.00 Error 12 900 75.00 Total 13 a. F 24.00 2,700 Determine the coefficient of determination.(Round your answer to 2 decimal places.) Coefficient of determination b. Assuming a direct relationship between the variables, what is the correlation coefficient? (Round your answer to 2 decimal places.) Coefficient of correlation c. Determine the standard error of estimate. (Round your answer to 2 decimal places.) Standard error of estimate #5The following sample observations were randomly selected. (Round your answers to 2 decimal places.) X: 4 5 3 6 10 Y: 10.8 12.6 9 14.4 19.6 a. The regression equation is formula17.mml = + X b. When X is 6 this gives formula17.mml = #6 The Airline Passenger Association studied the relationship between the number of passengers on a particular flight and the cost of the flight. It seems logical that more passengers on the flight will result in more weight and more luggage, which in turn will result in higher fuel costs. For a sample of 24 flights, the correlation between the number of passengers and total fuel cost was 0.721. 1. State the decision rule for 0.100 significance level: H0: 0; H1: > 0 (Round your answer to 3 decimal places.) Reject H0 if t > 2. Compute the value of the test statistic. (Round your answer to 3 decimal places.) Value of the test statistic 3. Can we conclude that the correlation in the population is greater than zero? Use the 0.100 significance level H0 . It is to conclude that there is positive association in the population between the two variables. #7 Pennsylvania Refining Company is studying the relationship between the pump price of gasoline and the number of gallons sold. For a sample of 18 stations last Tuesday, the correlation was 0.7. At the 0.01 significance level, is the correlation in the population greater than zero? (Round your answer to 3 decimal places.) The test statistic is . Decision: H0: 0 #8 On the first statistics exam, the coefficient of determination between the hours studied and the grade earned was 60%. The standard error of estimate was 19. There were 22 students in the class. Develop an ANOVA table for the regression analysis of hours studied as a predictor of the grade earned on the first statistics exam. (Round your decimal answers to 2 places.) SourceDF Regression Error Total SS MS