Regression coefficient- need help!!

#1
Suppose that we have regressed the log of household median income on the Gini coefficient and obtained the following result. Standard errors are listed in parenthesis.:
ln(median income)=11.26 − 1.43 ⋅Gini
(0.36) (0.80)
R2=0.061 no. obs.=51
F(1,49)=3.21 (p=0.079)

1. Interpret the regression coefficients.

2. Are the regression coefficients statistically significant from zero at the 10 percent significance level? Are they statistically significant from zero at the 5 percent significance level?

3. Given the values of R-squared and the F-statistic, how well do you think the model explains the variance in log of median income?
 

noetsi

Fortran must die
#2
This looks like homework and the rule here is to see some evidence that you are working on it before posters given answers. To start with you need to note whether you are using liner, logistic, or some other form of regression as answers will be different depending on which you are using.

I am not sure from your example what the slopes of the variable and the intercept are. For linear regression the slopes show the change in Y for a one unit change in X. The intercept shows the value of Y when all other X are 0. That is how you address one.

If the f test is signficant (as reflected by its p value) the model has predictive value. R squared shows explained variance. You have explained about 6 percent of the total variance. Do you think that is a lot of this phenomenon? If so you have a good model, although if the F test is not significant few would consider the model useful. This is how you address 3.

Normally you would intepret 2 through p values you do not list. You can use the the t scores and SE to get a general sense if a model is signficant (although I have not seen this done for the .1 level - I assume you can).