1)Compare results reported on page 4.14 and 4.18 of the lecture slides, write a few paragraphs to describe the differences.
When you look at both of the slides you can see that each slide has estimate, standard error, t value, and PR. The slides do differ, however. Slide 4.14 has sigma, beta1, and beta2 as their parameters. Whereas slide 4.18 has mu, theta1, and theta2 as its parameters. In slide 4.14 sigma represents the standard deviation for the data. Looking at the number -.065207 under the estimate column and the beta1 row, we know that this beta1 is the y-intercept, this shows where the regression line will start. When we look at the .037613 under the estimate column and beta2 row, we know that this represents the slope of the regression line. Beta2 also represents income. This slope will show that for every 1 unit increase in education that there will be a .37613 increase in income. Standard error is a measure of the statistical accuracy of an estimate. This shows the average of the values. The values come from the difference between the predictor line and actual values. In 205, we also learned about how to read whether or not something was statistically significant. When a PR value is lower, that means that you value has great statistical significance, and vice versa with the signer PR value.
In slide 4.18, mu represents known average which finds standard deviation. In this set of data, like beta1 in 4.14, theta1 in 4.18 (1.461011) represents the y intercept which is also where the regression line starts. For theta2 (.109081) represents the slope. This mean that like the other slide, for every 1 unit increase of education, there is an increase in income by .109081 in standard deviation. As we know, people with a higher level of education have a higher chance of higher income and those with lower levels of education often have lower levels of income.
2)In both models, if you introduce a second independent variable age, what do you think the relationship between age and income might be?
Mu and sigma would change if age was added to the two different models. In both of the models, only the relationship between income and education is being looked at. If you put in another variable such as age into this data set, then the correlation between both income and education would drop lower. Instead of having only two variables, you would have three different variables to be considered in the data. Naturally, as people become older in their working adult life, we see an increase income. But then there is a decline the older that people may get due to retirement and no longer being a part of the working force.