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Least Squares and Number of Banks

1.3 Exercises
6. Decrease in Banks The number of banks in the United
States has dropped about 30% since 1992. The following
data are from a survey in which x represents the years
since 1900 and y corresponded to the number of banks, in
thousands, in the United States.?
n=10 Ex2 = 93,205
Ex=965 Exy=9165.1
Ey=95.3 Ey2 =920.47

**note The E's are not E's but the funny shaped symbol like an E and the 2 after x and y are squares.

a. Find an equation of the least squares line.
b. If the trend continues, how many banks will there be in
2004?
c. Find and interpret the coefficient of correlation.

14.Poverty Levels The following table lists how poverty level
income cutoffs (in dollars) for a family of four have
changed over time.?

Year Income
1970 3968
1975 5500
1980 8414
1985 10,989
1990 13,359
1995 15,569
2000 17,603

Let x be the year, with x=0 corresponding to 1970, and y be the income in thousands of dollars. (Note Ex=105, Ex2 =2275, Ey=75.402, Ey2=968.270792, Exy=1460.97.)
**note The E's are not E's but the funny shaped symbol like an E and the 2 after x and y are squares

a. Plot the data. Do the data appear to lie along a straight
line?
b. Calculate the coefficient of correlation. Does your result
agree with your answer to part a?
c. Find the equation of the least squares line.
d. Use your answer from part c to predict the poverty level
in the year 2015.

16. Air Conditioning While shopping for an air conditioner,
Adam Bryer consulted the following table giving a
machine's BTUs and the square footage that it would
cool.

ft2(x) BTUs ( y)
150 5000
175 5500
215 6000
250 6500
280 7000
310 7500
350 8000
370 8500
420 9000
450 9500

a. FInd the equation for the least squares line for the data.
b. to check the fit of the data to the line, use the results from part a to find the BTUs required to cool a room of 150 ft2, 280 ft2, and 420 ft 2. How well does the actual data agree with the predicted values?
c. Suppose Adam's room measures 230 ft2. Use the results from part a to decide how many BTUs it requires. If air conditioners are available only with the BTU choices in the table, which would Adam choose?
d. Why do you think the table gives ft2 instead of ft3, which would give the volume of the room?

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Solution Summary

This provides an example of finding a least squares line for data, checking the fit, and using the line.

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