.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?

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

Step-by-step explanation:

Regression is given by :

Obese Rate = 25.6 - 0.001Log_Soda Tax.

coefficient of Log_Soda Tax given = -0.001. Thus, we have to interpret this coefficient.

Representing ObeseRate as O and Log_Soda Tax be represented as 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)

Thus, coefficient of Soda tax is interpreted as follows

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

(b)

R² = 0.35

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

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

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step-by-step explanation: