Question

5.A researcher has data for 33 states' data on soda taxes and obesity rate (percent of people who are obese), Soda taxes measured in cents, and estimates the following regression (Note that log value of soda tax is used as the independent variable). Standard errors are in parentheses ObeseRate=25.6 - 0.001 Log_SodaTax R2 = 0.35 (10.0) (0.002) 1) How would you interpret the estimated coefficient of SodaTax? 3) R2 = 0.35 in the above estimated regression, how would you interpret it?

Answer 1

Answer 5

(1)

Regression is given by :

ObeseRate = 25.6 - 0.001Log_Soda Tax.

Here coefficient of Log_Soda Tax = -0.001. Hence we have to interpret this coefficient.

Let for simplicity, ObeseRate be represented by O and Log_Soda Tax be represented by Log(S)
=> O = 25.6 - 0.001Log(S)

dO/dLS = -0.001(1/S)

=> dO = -0.001(dS/S)

=> dO = -(0.001*100)(dS/S)/100

=> dO = -0.00001(% change in S)

Note that (dS/S)*100 = % change in S

Thus if we increase S by 1%, then dO = -0.00001i.e. O will decrease by 0.00001 units(negative sign means that O decreases)

Hence coefficient of Soda tax is interpreted as follows

1 percent increase in soda tax rate will result in decrease in obesity rate by 0.00001 percent.

(b)

R² = 0.35

R² is interpreted as the percentage of variation in dependent variable is explained by explanatory variable.

Here R² = 0.35 means that 35% of variation in Obesity rate is explained by log of soda taxes.