46 The average new car cost for the years from 1975 to

46
The average new car cost for the years from 1975 to 2000 is given in the table where x is the number of years since 1900?
Year (x)
75
80
85
90
95
00
Cost (y)
6000
7500
12000
16000
20400
24900
a. Find an equation for the least squares line.
b. Use your equation from part a to predict the average cost of a new car in the year 2005. (x = 105)
c. Find and interpret the coefficient of correlation. Does it indicate that the line is a good fit for the data?
d. Plot the data. Does the scatterplot suggest the trend might not be linear?
It is very important that all work is shown. I would also appreciate it if you would highlight the answer. Thanks!
(please see # 48 on second page)
48
The following system of equations is given.
a. Solve by the echelon method.
b. Solve by the Gauss-Jordan method.
c. Write the system as a matrix equation AX = B
d. Find the inverse matrix A from part C.
e. Solve the system using A-1 from part d.