b. How much does the average private college tuition increase when the average p

Question

b. How much does the average private college tuition increase when the average public college tuition increases by $100?

c.

When the average public college tuition reaches $8,500 for the independent variavle how much would you expect the average private college tuition to be? The data shown below indicate the average tuition (in dollars) over a six-year period for private and public colleges in a region. Complete parts a through c below. Year Private 8,61710,436 2,193 15,658 18,90 20,788 Public 2057 2.3653,124 3,6324,678 5,663 4 a. Conduct a simple linear regression analysis of these data in which the average tuition for private colleges is predicted by the average public college tuition. Test the significance of the model using = 0.05. What is the estimated regression slope coefficient? b,- (Round to two decimal places as needed.)

Explanation / Answer

Here to evalute the least square regression line, we require values of x, y . xy. x2

so the table to evluate all these value is given below

Here if we assume that x = public college tuiton fee and y = private college tuition fee.

Here n = 6

so if the linear regression equation is

y^ = a + bx

where

a = [(y) (x2 ) - (x) (xy)]/ [ n (x2 ) - (x)2 ]

a= [ 86593 * 86587527 - 21489 * 343195339] / [ 6 * 86587527 - 214892]

a = 2129.061

b = [ n(xy) - (x)((y)]/ [ n (x2 ) - (x)2 ]

b = [ 6 * 34195339 - 21489 * 86593] / [ 6 * 86587527 - 214892]

b = 3.4352

(a) Estimated regression slope coefficient = 3.4352 or 3.44

Here standard error se = 0.2835

t = 3.4352/ 0.2835 = 12.1187 > tcritical ( tcritical = 2.7764 )

so slope is significant here.

(b) Here if the average public college tuition increase by $ 100, then there will be increase of 3.4352 * 100 = $ 343.52 .

(c) Here if x = $ 8500

then y^ = 3.4352 * 8500 + 2129.061 = $ 31328.26

Public(x) Private (y) x^2 xy 2057 8617 4231249 17725169 2335 10436 5452225 24368060 3124 12193 9759376 38090932 3632 15658 13191424 56869856 4678 18901 21883684 88418878 5663 20788 32069569 117722444 Sum 21489 86593 86587527 343195339

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