Observed and Simulated data difference and prediction of unseen data

[ameshaspanta]

I am very new to using pymc and Bayesian linear regression, and I am currently following the documentation provided in pymc 5.7.0 here to predict a target value using seven predictors.These predictors are not highly correlated with the target variable. However, the results I obtained from the model are disappointing, and I am unsure about how to tune the parameters or how to initialize the priors to improve the model’s performance.
Also, I am not sure how to use this model to predict the unseen data and plot HDI for them.
I appreciate any help or advice!
Here are the snapshot of the results, and the data:

N, D = x_train.shape
D0 = int(D / 2) 
import pytensor.tensor as at
with pm.Model(coords={"predictors": x_train.columns.values}) as test_drn_model:
    # Prior on error SD
    sigma = pm.HalfNormal("sigma", 20)
    # Global shrinkage prior
    tau = pm.HalfStudentT("tau", 2, D0 / (D - D0) * sigma / np.sqrt(N))    
    # Local shrinkage prior
    lam = pm.HalfStudentT("lam", 2, dims="predictors")
    c2 = pm.InverseGamma("c2", 1, 0.1)
    z = pm.Normal("z", 0.0, 1.0, dims="predictors")   
    # Shrunken coefficients
    beta = pm.Deterministic(
        "beta", z * tau * lam * at.sqrt(c2 / (c2 + tau**2 * lam**2)), dims="predictors")
    # No shrinkage on intercept
    beta0 = pm.Normal("beta0", 100, 25.0)
    Value = pm.Normal("Value", beta0 + at.dot(x_train.values, beta), sigma, observed=y_train.values)

with test_drn_model:
    idata = pm.sample(1000, tune=2000, random_seed=42, target_accept=0.99)