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# Demand estimation: multiple regression

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1. Using a multiple regression program available on a computer to which you have access, estimate the coefficients of the demand for the data given in table 1
2. Provide a economic interpretation for each of the coefficients in the regression equation you have computed.
3. What is the Value of the coefficient of determination? How would you interpret this result?

STA Data on Transit Ridership

Year Weekly Riders (Y) (x 1,000) Price (P) per Ride (Cents) Population (T) (x 1,000 Income (I) Parking Rate (H) (Cents)

1966 1200 15 1800 2900 50
1967 1190 15 1790 3100 50
1968 1195 15 1780 3200 60
1969 1110 25 1778 3250 60
1970 1105 25 1750 3275 60
1971 1115 25 1740 3290 70
1972 1130 25 1725 4100 75
1973 1095 30 1725 4300 75
1974 1087 30 1720 4400 75
1975 1087 30 1705 4600 80
1976 1080 30 1710 4815 80
1977 1020 40 1700 5285 80
1978 1010 40 1695 5665 85
1979 1010 40 1695 5800 100
1980 1005 40 1690 5900 105
1981 995 40 1630 5915 105
1982 930 75 1640 6325 105
1983 915 75 1635 6500 110
1984 920 75 1630 6612 125
1985 940 75 1620 6883 130
1986 950 75 1615 7005 150
1987 910 100 1605 7234 155
1988 930 100 1590 7500 165
1989 933 100 1595 7600 175
1990 940 100 1590 7800 175
1991 948 100 1600 8000 190
1992 955 100 1610 8100 200

See attached word and excel file.

#### Solution Preview

You have run a simple regression with each of the independent variables, one at a time. The question is asking you for multiple regression which means that you run a regression for all the independent variables at the same time.

I have run the regression for you, look at the attached excel file. I am giving the result here.

The process is the same as in simple regression, the only difference is that you select all the independent variables at the same time.

Coefficients
Intercept 80.78980124
Price (P) per Ride -1.612847077
Population (T) 0.646142088
Income (I) -0.047419294
Parking Rate (H) 1.943769135

This means that you can write the regression equation as
Y=80.7898 -1.6128 P + 0.6461 T - 0.0474 I + 1.9437 H

Where
Y = Weekly Riders in thousands
P= Price per Ride in ...

#### Solution Summary

The solution runs a multiple regression model to estimate the coefficients of the demand for the data given (STA Data on Transit Ridership) provides conomic interpretation of the coefficients, and calculates the value of the coefficient of determination.

\$2.19