Econometrics Case

Econometrics

1) What is the meaning of

(a) Statistical inference

Statistical inference is the process of making an estimate, prediction, or decision about a population based on sample data. Populations may be too large that investigating each member of the population would be impractical, expensive and time consuming.

(b) Random variable

A random variable or stochastic variable is a variable whose value is determined by the outcome of a random experiment.

(c) Covariance (provide explanation)

Covariance is a special kind of value that measure how 2 random variables vary or move together.

The covariance between two random variables can be

o Positive (if they move in the same direction);

o zero (if there is no relationship between them) or;

o Negative (if they move in different direction).

cov(X,Y) = E[(X - EX)(Y-EY)]

(d) Correlation (provide explanation)

The correlation coefficient measures how strongly two variables are related or associated.

Correlation is a pure number falling between -1 and 1.

Correlation close to +1, means 2 variables are very strongly positively correlated. Correlation close to -1, means 2 variables are very strongly negatively correlated. Correlation close to zero, means 2 variables are not related.

2) Suppose that you are asked to conduct a study to determine whether smaller class sizes improve performance on standardized tests of fourth graders in Sarawak.

(a) If you could conduct any experiment you want, what would you do? Be specific.

Ideally, we could randomly assign students to classes of different sizes. That is, each student is assigned a different class size without regard to any student characteristics such as ability and family background. We also would like substantial variation in class sizes.

(b) More realistically, suppose you can collect observational data on several thousand fourth graders. You can obtain the size of their fourth-grade class and a standardized test score taken at the end of fourth grade. Why might you expect a negative correlation between class size and test score? Explain.

A negative correlation means that larger class size is associated with lower performance. We might find a negative correlation because larger class size actually hurts performance. However, with observational