I have the following regression equation to predict house prices: $PRICE_i=\beta_1+\beta_2LIV_i+\beta_3LOT_i+\beta_4ROOMS_i+\beta_5BATHS_i+\beta_6YEAR_i+u_i$
I need to test the 5 different hypotheses that each individual explanatory variable is statistically significantly different from zero. i.e. $H_0: _ = 0$ where $ = 2, 3, 4, 5, 6$.
To do this, can I use the following equation $\frac{b\ -\ \beta}{SE_b}$ where b is the coefficient of the variable and $\beta$ in this case will be $0$. I have all of the coefficients and standard errors. I will use this equation to see whether the result lies within the acceptance/rejection region based on the t-test critical value.
My question is does the critical value remain the same for all of these tests? or do I need to find a new critical value for each test based on the degrees of freedom?
One standard way to do this is to run reduced models. For example, if you want to test whether your $\beta_2=0,$ you would run the reduced model $$PRICE_i=\beta_1+\beta_3LOT_i+\beta_4ROOMS_i+\beta_5BATHS_i+\beta_6YEAR_i+u_i.$$ You get your standard squared error from the complete model, $SSE_C,$ and compare it with the (usually larger) $SSE_R$ from the reduced model, and then use an $F$ test for the final results as follows: $$F=\frac{(SSE_R-SSE_C)/(\#\beta_C - \#\beta_R)}{SSE_C/(\#\text{data points} - \#\beta_C)}.$$ The $F$ distribution has $\#\beta_C - \#\beta_R$ numerator d.o.f., and $\#\text{data points} - \#\beta_C$ denominator d.o.f.