Plot these data and determine whether a linear model is

Question

Problem 1:

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:

Students	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	73	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.

Problem 2:

Using the data in problem 1 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.

Key Equations

MSR = SSR / K

Mean square regression. K is the number of independent varisbles.

Problem 3:

Using the computer software, find the least squares regression line for the data in problem 1. Based on the F test, is there is a statistically significant relationship between the test grade and final average in the course?

Key Equations

F = MSR / MSE

F statistic used to test significance of overall regression model.

Problem 4:

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:

	Number of
Year	Tourists	Ridership
	(1,000,000s)	(100,000s)
1	7	15
2	2	10
3	6	13
4	4	15
5	14	25
6	15	27
7	16	24
8	12	20
9	14	27
10	20	44
11	15	34
12	7	17

(a) Plot these data and determine whether a linear model is reasonable.

(b) Develop regression model

(C) What is expected ridership if 10 million tourists visit the city?

(d) If there are no toruists at all,explain the predicted ship.