Life will become easiwe when you get to the point of importing your Excel files into data frames or tables and are able to provide reproducible examples, called reprex.

Let's take an example from the help(lm) page:

require(graphics)
## Annette Dobson (1990) "An Introduction to Generalized Linear Models".
## Page 9: Plant Weight Data.
ctl <- c(4.17,5.58,5.18,6.11,4.50,4.61,5.17,4.53,5.33,5.14)
trt <- c(4.81,4.17,4.41,3.59,5.87,3.83,6.03,4.89,4.32,4.69)
group <- gl(2, 10, 20, labels = c("Ctl","Trt"))
weight <- c(ctl, trt)
lm.D9 <- lm(weight ~ group)
summary(lm.D9)
Call:
lm(formula = weight ~ group)
Residuals:
Min 1Q Median 3Q Max
-1.0710 -0.4938 0.0685 0.2462 1.3690
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.032 0.220 22.85 9.5e-15 ***
groupTrt -0.371 0.311 -1.19 0.25
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.696 on 18 degrees of freedom
Multiple R-squared: 0.0731, Adjusted R-squared: 0.0216
F-statistic: 1.42 on 1 and 18 DF, p-value: 0.249

The "equation" is given in Call. The meaning of other parts of the output are explained in one of my posts.

However, you should review the concept of linear regression with aids such as this to understand that \mu and \sigma don't map over from the normal distribution in any way that will be useful to your understanding of linear regression.