Repeat the Problem in I using Logarithmic transformation. For example, In y = be
ID: 3157622 • Letter: R
Question
Repeat the Problem in I using Logarithmic transformation. For example, In y = beta_0 + beta_1 In X_1 + beta_2 In X_2.. + mu. In this case, you can obtain general elasticities from beta_i S. So Question 7 should be "Calculate the price elasticity of demand." and Question 8 should be "Calculate the income elasticity of demand". Demand Estimation Early in 1993, the Southeastern Transportation Authority (STA), a public agency responsible for serving the commuter rail transportation needs of a large Eastern city, was faced with rising operating deficits on its system. Also, because of a fiscal austerity program at both the federal and state levels, the hope of receiving additional subsidy support was slim. The board of directors of STA asked the system manager to explore alternatives to alleviate the financial plight of the system. The first suggestion made by the manager was to institute a major cutback in service. This cutback would result in no service after 7:00 P.M., no service on weekends, and a reduced schedule of service during the midday period Monday through Friday. The board of STA indicated that this alternative was not likely to be politically acceptable and could only be considered as a last resort. The board suggested that because it had been over five years since the last basic fare increase, a fare increase from the current level of $1 to a new level of $1.50 should be considered. Accordingly, the board ordered the manager to conduct a study of the likely impact of this proposed fare hike. The system manager has collected data on important variables thought to have a significant impact on the demand for rides on STA. These data have been collected over the past 24 years and include the following variables: Price per ride (in cents) - This variable is designated P in Table 1. Price is expected to have a negative impact on the demand for rides on the system. Population in the metropolitan area serviced by STA -It is expected that this vari able has a positive impact on the demand for rides on the system. This variable is designated T in Table 1. Disposable per capita income - This variable was initially thought to have a positive impact on the demand for rides on STA. This variable is designated I in Table I Parking rate per hour in the downtown area (in cents) - This variable is expcctcdi to have a positive impact on demand for rides on the STA. It is designated H in Table 1. The transit manager has decided to perform a multiple regression on the data to determine the impact of the rate increase. What is dependent variable in this demand study? What are the independent variables? What are expected signs of the variables thought to affect transit ridership on STA Using a multiple regression program available on a computer to which you have access, estimate the coefficients of the demand model for the data given in Table 1. Provide an economic interpretation for each of the coefficients in the regression equation you have computed What is the value of the coefficient of determination? How would you interpret this result? Calculate the price elasticity using 1992 data. Calculate the income elasticity using 1992 data. If the fare is increased to $ 1.50, what is the expected impact on weekly revenues to the transit system if all other variable remain at their 1992 levels?Explanation / Answer
1. The dependent variable is the weekly rides.
2. The independent variables are the year number, Price, Population, Income, and Parking.
3. As the year and population grows, the weekly rides is supposed to increase and as the price, income, and parking costs go up, the rides are expected to decline.
4. The R program gives the answer:
> tt <- read.csv("clipboard",sep=" ")>
> names(tt)
[1] "Year" "Weekly.Rides" "Price" "Population" "Income"
[6] "Parking"
> wrlm <- lm(log(Weekly.Rides)~log(Year)+log(Price)+log(Population)+log(Income)+log(Parking),data=tt)
> summary(wrlm)
Call:
lm(formula = log(Weekly.Rides) ~ log(Year) + log(Price) + log(Population) +
log(Income) + log(Parking), data = tt)
Residuals:
Min 1Q Median 3Q Max
-0.027564 -0.009774 -0.000973 0.010077 0.038149
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -199.93315 50.97760 -3.922 0.000783 ***
log(Year) 27.05042 6.61645 4.088 0.000526 ***
log(Price) -0.14972 0.02657 -5.635 1.36e-05 ***
log(Population) 0.53957 0.45981 1.173 0.253748
log(Income) -0.21185 0.05445 -3.891 0.000843 ***
log(Parking) -0.01816 0.02888 -0.629 0.536250
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.01784 on 21 degrees of freedom
Multiple R-squared: 0.9687, Adjusted R-squared: 0.9612
F-statistic: 130 on 5 and 21 DF, p-value: 4.633e-15
The estimated coefficients are given in bold font above.
5. On the log-scale, the variables Price, Income, and Parking have a negative impact as expected, while Year and Population are having positive impact,again as expected.
6. The coefficient of determination is 0.9612 or about 96% which means that the chosen variables have a very good explanation of the number of rides.
7 The price elasticity using 1992 data is log(100)* -0.14972 = -0.6895.
8. The income elasticity using 1992 data is log(8100)*-0.21185 = -1.9066.
9. The prediction is
> exp(sum(wrlm$coefficients *c(1,log(1992),log(101.5),log(1610),log(8100),log(200))))
[1] 949.2879