# Interpreting regression results

I have a few different regression results, and need some help interpreting them. On a few, I put some of my answers to the questions in brackets - I'd like to know if I am correct, if not, some assistance would be appreciated.

The results are as follows

A. PSoda Hat = .956 + .1149882 PrBlack + 1.60 income

Where:

P Soda is the price of soda

Pr Black is the proportion of the population that is black

Hat = an estimated value

---- How do we interpret the coefficient on PrBlack? {I interpreted it as a 1% increase in the proportion of black population increases the price of soda by 11.49%}

-- How does this estimate in A compare to the output:

PSoda Hat = 1.037 + 0.6492 PrBlack {I interpreted this as areas with a proportion of black population spend 6.49% more on soda, all else equal. The previous model estimated provides us with a greater coefficient on the income variable than this one}

B. Log (P Soda) Hat = -.7937 + .1215 Pr Black + .765 Log (income)

---How doe we interpret the effect of Pr Black

I add the variable PPov (proportion in poverty) to the model in B and estimate the following:

Log (P Soda) Hat = -1.46 + .07280 Pr Black + .136 Log (income) + .3803 PPov

----What happens to the coefficient of Pr Black, and does it make sense?

C. The correlation between log(income) and PPov is -.8648 ... does this affect the model estimated above?

#### Solution Preview

A. PSoda Hat = .956 + .1149882 PrBlack + 1.60 income

Where:

P Soda is the price of soda

Pr Black is the proportion of the population that is black

Hat = an estimated value

---- How do we interpret the coefficient on PrBlack?

The proportion is a value from 0 to 1 and the price of the Sada is in ($). If it is in cents, please revise it.

An increase in the proportion of black population by 1 increases the price of the soda by 0.1149 dollars.

Interpreted differently, a increase in proportion of black population by 0.01 will increase the price of soda by 0.1149 cents

-- How does this estimate in A compare to the output: ...