Complete Problems 4-13, 4-14, 4-15, and 4-19. Use Excel's regression option to perform the regression. Use an Excel spreadsheet file for the calculations and explanations, with one worksheet per problem. Use the problem number for each worksheet name. Cells should contain the formulas (i.e., if a formula was used to calculate the entry in that cell). 4-13 Students in a management science class have just received their grades on the first test. The instructor has provided information about the first test grades in some previous classes as well as the final average for the same students. Some of these grades have been sampled and are as follows: STUDENT 1 2 3 4 5 6 7 8 9 1st test grade 98 77 88 80 96 61 66 95 69 Final average 93 78 84 73 84 64 64 95 76 (a) Develop a regression model that could be used to predict the final average in the course based on the first test grade. (b) Predict the final average of a student who made an 83 on the first test. (c) Give the values of r and r^2for this model. Interpret the value of r^2 in the context of this problem. 4-14 Using the data in Problem 4-13, test to see if there is a statistically significant relationship between the grade on the first test and the final average at the 0.05 level of significance. Use the formulas in this chapter and Appendix D. 4-15 Using computer software, find the least squares regression line for the data in Problem 4-13. Based on the F test, is there a statistically significant relationship between the first test grade and the final average in the course? 4-19 Bus and subway ridership in Washington, D.C., during the summer months is believed to be heavily tied to the number of tourists visiting the city. During the past 12 years, the following data have been obtained: YEAR 1 2 3 4 5 6 7 8 9 10 11 12 NUMBER OF TOURISTS (1,000,000s) 7 2 6 4 14 15 16 12 14 20 15 7 RIDERSHIP (100,000s) 15 10 13 15 25 27 24 20 27 44 34 17 (a) Plot these data and determine whether a linear model is reasonable. (b) Develop a regression model. (c) What is expected ridership if 10 million tourists visit the city? (d) If there are no tourists at all, explain the predicted ridership