I have fittet a glm in R with the results

> glm1 <- glm(log(claims)~log(sum)*as.factor(grp),family=gau ssian(link="identity"))
> summary(glm1)

Call:
glm(formula = log(claims) ~ log(sum) * as.factor(grp), family = gaussian(link = "identity"))

Deviance Residuals:
Min 1Q Median 3Q Max
-6.6836 -1.3626 -0.2576 1.2038 8.2480

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.525657 0.436102 8.084 8.18e-16 ***
log(sum) 0.334288 0.025668 13.024 < 2e-16 ***
as.factor(grp)2 0.434262 0.976240 0.445 0.6565
as.factor(grp)3 3.666490 1.436471 2.552 0.0107 *
as.factor(grp)4 0.040782 1.024730 0.040 0.9683
log(sum):as.factor(grp)2 0.007719 0.061914 0.125 0.9008
log(sum):as.factor(grp)3 -0.209986 0.091578 -2.293 0.0219 *
log(sum):as.factor(grp)4 0.059342 0.067320 0.881 0.3781
---
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1

(Dispersion parameter for gaussian family taken to be 3.693731)

Null deviance: 15839 on 4035 degrees of freedom
Residual deviance: 14878 on 4028 degrees of freedom
AIC: 16737

Number of Fisher Scoring iterations: 2

But i'm not sure what I get out of the summary. What does it tell me?

Is it something like

Y=0.334288*X_sum+0.434262*X_2

and what can I conclude? What is Y, can anyone help me please