A previous exercise discussed the relationship between the average college tuition (in 2003 dollars) for private and public colleges. The data indicated in the article follow:

a. Construct the regression equation that would predict the average college tuition for private colleges using that of the public colleges.
b. Determine if there is a linear tendency for the average college tuition for private colleges to increase when the average college tuition for public colleges increases. Use a significance level of 0.05 and a p -value approach.
c. Provide a 95% confidence interval for the average college tuition for private colleges when the average college tuition for public colleges reaches $7,000.
d. Is it plausible that the average college tuition for private colleges would be larger than $35,000 when the average college tuition for public colleges reaches $7,000? Support your assertion with statistical reasoning.

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Period 983-1984 1988-1989 993-1994 Private 9.202 Public Period 998 1999 2003 2004 2008 2009 Private 16.454 Public 12,146 2.395 13,844 3,188 2,074 19.710 4.694 21,582 5,652 3.632