The table shows the average cost of tuition and fees y in dollars at 4-year public colleges.

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The table shows the average cost of tuition and fees y in dollars at 4-year public colleges. In this table x = 0 represents 1980 and x = 20 corresponds to 2000.image


These data can be modeled by using linear regression. Ideally, we would like f(x) = ax + b to satisfy the following five equations.image


Since the data points are not collinear, it is impossible for the graph of a line to pass through all five points. These five equations can be written asimage


The least-squares solution is found by solving the normal equationsimage


for X. The solution is X= (ATA)-1ATB. Using technology, we find a = 138.16 and b = 693.8. Thus f is given by the formula f(x) = 138.16x + 693.8. The function f and the data can be graphed. See the figure.image


Solve the normal equations to model the data with the line determined by f(x) = ax + b. Plot the data and f in the same viewing rectangle.



The table shows average cost of tuition and fees y in dollars at private 4-year colleges. In this table x = 0 corresponds to 1980 and x = 20 to 2000.image

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