Can someone check my assignment please?

[eminaker]

ln⁡(Y)=β0+β1ln⁡(L)+β2ln⁡(K)
The data given is taken from the Penn World Table 9.1 and includes the following variables for Turkey from 1970 to 2017:
Income (Y) is taken as rgdpna (Real GDP at constant 2011 national prices (in mil. 2011US$))
Labor (L) is taken as emp (Number of persons engaged (in millions))
Capital (K) is taken as rnna (Capital stock at constant 2011 national prices (in mil. 2011US$))

Estimate and report the parameters of the production function model 

(β0 ) ̂=-2.852e+04 (β1 ) ̂=1.144e+04 (β2 ) ̂=2.746e-01

My finding:

summary(model)

Call:
lm(formula = Y ~ K + L, data = TableTR)

Residuals:
Min 1Q Median 3Q Max
-77352 -24079 1796 17203 80133

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.852e+04 9.089e+04 -0.314 0.755
K 2.746e-01 1.953e-02 14.062 <2e-16 ***
L 1.144e+04 8.103e+03 1.412 0.165

Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 34240 on 45 degrees of freedom
Multiple R-squared: 0.9954, Adjusted R-squared: 0.9952
F-statistic: 4830 on 2 and 45 DF, p-value: < 2.2e-16

The question I couldn't solve is the following:

Test whether there are constant returns to scale or not.
Hint: One of the models is false. You need to estimate the correct one that abides the restriction β1+β2=1

(ln⁡(Y/L) ) ̂=β0+β1ln⁡(K/L) | (ln⁡(Y/K) ) ̂= β0+β1ln⁡(K/L)

[technocrat]

Hi, and welcome!

A couple of preliminaries. Please see the homework policy and use reproducible examples, reprex .

A reprex almost always needs to include a dataset that will work with the code. It doesn't have to be the full dataset, just an extract or, ideally, a standard data() object that is similar or you can adjust to make similar. mtcars is popular for that purpose.

For your problem, there are two tools that may prove helpful:

str(model)
coef(model)