# application of the least-squares procedure

The application of the least-squares procedure to a multiple linear regression equation requires that:

a no exact linear relationships can exist among any of the independent variables

b the number of observations (n) must exceed the number of b parameters to be estimated (m)

c the number of observations (n) must exceed the number of parameters to be estimated (m + 1)

d a and b

e a and c

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#### Solution Summary

Demonstrate the application of the least-squares procedure.

Least squares

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?