How do I extract estimates and standard errors as a measure of linear increment from an lm model in R?

Let's say I have data:

data = data.frame(xdata = 1:10, ydata = 6:15)

I look at the data

data

  xdata ydata
1      1     6
2      2     7
3      3     8
4      4     9
5      5    10
6      6    11
7      7    12
8      8    13
9      9    14
10    10    15

Now I want to include a third column to the data which should be an increment/estimate and a fourth column we should be standard errors. To do this, I estimate the increment for each row of the data by fitting a linear model and taking the slope/estimate and also the associated standard error. So I fit model_1:

model_1 = lm(ydata~xdata,data = data)
out = summary(model_1)
out

It gives me:

Call:
lm(formula = ydata ~ xdata, data = data)

Residuals:
       Min         1Q     Median         3Q        Max 
-5.661e-16 -1.157e-16  4.273e-17  2.153e-16  4.167e-16 

Coefficients:
             Estimate Std. Error   t value Pr(>|t|)    
(Intercept) 5.000e+00  2.458e-16 2.035e+16   <2e-16 ***
xdata       1.000e+00  3.961e-17 2.525e+16   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.598e-16 on 8 degrees of freedom
Multiple R-squared:      1, Adjusted R-squared:      1 
F-statistic: 6.374e+32 on 1 and 8 DF,  p-value: < 2.2e-16

To extract the estimate, I can simply do:

out$coefficients[2,1]

To extract the standard error, I can simply do:

out$coefficients[2,2]

but my interest is to have an out put that shows estimates and standard errors for each row so that I end up with 10 estimates and 10 standard errors. Is there a way to do this?

Many thanks!