# Demand estimation: multiple regression

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.

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#### 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.