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# bayesian linear regression predicted outcomes

hello jaspers,

I wonder if someone can help me understand predicted outcomes of Bayesian linear regression models.

i analyzed the effect of relative humidity on weight loss of flour beetles using Bayesian simple linear regression. the results showed an intercept of 6.022 and a slope of -0.052. given the intercept and slope i need to estimate the predicted weight loss for each beetle. the Bayesian student guide gives the prediction equation as y = b0 + b1*x1, where,

y = estimated dependent outcome variable score,

b0 = constant (intercept),

b1 = regression coefficient

x1= score difference for the independent predictor variable (= x – mean x)

the mean relative humidity is 50.389.

if a flour beetle has observed values of 3.72 for weight loss and 93 for relative humidity, then the predicted weight loss = 6.022 + (-0.052*[ 93 – 50.389]) = 3.806

is the predicted weight loss of 3.806 the mean of a normal distribution of predicted values for this flour beetle? If it is, then how is the 95% credible interval calculated?

cheers

• Hi Narcilili,

I'm assuming that you have a single linear regression model (no model-averaging).

is the predicted weight loss of 3.806 the mean of a normal distribution of predicted values for this flour beetle? If it is, then how is the 95% credible interval calculated?

That depends a bit on what you want to do. If you want to use the posterior means for b0, b1, and the standard deviation of the residuals, then you have that the predicted weight loss at those observed values is a normal distribution with mean 3.806 and standard deviation equal to that of the residuals. From there on you can use the standard way to compute a uncertainty interval for a normal distribution to obtain the credible interval.

On the other hand, if you want to look at the posterior predictive distribution, then you need the raw mcmc samples for b0, b1, and the standard deviation of the residuals. Then you can simulate a new value for each mcmc sample. Those samples form a distribution, and then you'd examine the quantiles of that distributions to obtain a credible interval.

Usually, the posterior predictive approach is more appropriate, although this might be a bit more work.

Cheers,

Don

• hello don,

thank you very much for responding. can JASP do the two methods you mentioned? let me show you a snippet of the b0 and b1 means

i wonder if you could show me how to do the two methods. thanks.

cheers