Now, lets say that I observe two more people and I see that they also have IQs of 110. So we have three people with IQs of 110. How does the variance of my estimate change from my prior? We can do this in the code by setting:

 
 
 
 
 

The variance should decrease. If we run the code, we can see that the width of the distribution decreases indicating the variance of the estimate also decreased

Other Questions Of This Category

If I observe now five people: the first three have an IQ of 110, and the last two have an IQ of 125, which of the following are true?

Let's say that we observe a person with an IQ of 125, as we did in the lecture. Which way should the posterior distribution, after our Bayesian update, shift?

For this problem, we are going to be using the above code to recreate some of the mathematics behind the Introduction to Bayesian Statistics lecture. The math has already been worked out for you, so…

A 95% confidence interval for the mean brain weight for all adults in 1905 with a head size of 3400 cm3 was calculated to be (1210.14 grams, 1232.33 grams). How would the width of the 95% prediction…

Next, a model is fit adding Age as an additional covariate to BMI as the variables predicting smoking status. The output is here: What does the coefficient of 0.0169 mean in context?

NHANES records whether an individual has smoked 100 cigarettes or more. The next few questions will focus on fitting models to predict whether someone has smoked 100+ cigarettes. First, a model is fit…

What distribution do the true errors need to follow in order to perform various inference procedures in linear regression?

You are interested in estimating the relationship between gender (the IV) and a binary indicator of ever having experienced a major depressive disorder (the DV), where both variables were collected…

What is the posterior mean after observing three people with an IQ of 110 in a row?

The 95% confidence interval for the coefficient for Age is given above as (0.014, 0.020). If instead we wanted a 90% confidence interval, how would the width of the interval change?

A 95% confidence interval for the mean brain weight for all adults in 1905 with a head size of 3400 cm3 was calculated to be (1210.14 grams, 1232.33 grams). How would the width of the 95% confidence…

What most likely happened to our R-Squared value when we added the third predictor LSTAT to our initial model?

After publishing a research paper describing the results from the model fitted for Question #3, you are contacted by 20 other large hospitals, and they wish to contribute to the estimation of a model…

Fill in the blanks. With 95% confidence, I estimate that the increase in log odds of smoking 100+ cigarettes for each increase by one in BMI, while holding Age constant, is between ____ and ____, on…

You wish to fit a model to a "forced choice" binary dependent variable measuring political party preference (if you had to pick a political party, which would you select: Democratic or Republican?),…