Ch3 Verified Test Bank Bivariate Ols: The Foundation Of

Chapter 3

True and False Questions:

1. True or False: The residual for observation i is e_ihat = Y_ihat - Y_i
2. True or False: The probability a continuous random variable is near some value is defined by its probability density function.
3. True or False: Violating the homoscedasticity condition will cause our OLS estimates of ₁hat to be biased.
4. True or False: Outliers are a bigger problem when we have a smaller sample size than when we have a bigger sample size.
5. True or False: The higher the correlation of the error term and the independent variable, the closer the expected value of B1hat is to the true value.
6. True or False: The higher the variance of X in our sample, the higher the variance of B1hat.

Multiple Choice Questions:

1. Suppose we estimate a model in which salary in thousands of Euros is the dependent variable and years of education is the independent variable. We get a result that says Income-hat = 20 + 2 Years Education. Which of the following is correct:
   1. Two years of education increases income by one.
   2. An extra year of education is expected to increase income by 2.
   3. An individual with 10 years of education is expected to have an income of 20.
   4. The expected income for someone with 0 years of education is 2.
2. A residual measures:
   1. The unobservable error term, .
   2. The distance between the actual value and the predicted value.
   3. The distance between -hat and the actual value of .
   4. The expected value of the dependent variable.

• 1. B1hat will be positive if Y tends to be above its mean when X tends to be above its mean.
  2. The sign of B1 will be the same sign as the denominator.
  3. Xi can never equal X-bar for any observation
  4. B1hat will be positive if Xi is always above X-bar.

1. In OLS with a large sample, the coefficient estimates will be:
   1. Correct
   2. Normally distributed.
   3. Centered on zero.
   4. Correct
2. An estimate of beta1 is said to be unbiased if
   1. Beta1-hat is normally distributed
   2. The coefficient distribution is narrow.
   3. The average value of the distribution of B1-hat is equal to the true value.
   4. The coefficient distribution is wide.
3. Name the concept: The variance of e_i is the same for every observation.
   1. Homoscedasticity
   2. Heteroscedasticity
   3. Consistency
   4. Bias
4. Which of the following are used to describe the goodness of fit for a model?
   1. The coefficient of the regression
   2. R²
   3. The standard error of the coefficient
   4. The constant
5. Imagine we have two separate models, Model 1 and Model 2. The R² for Model 1 is 0.8 and the R² for Model 2 is 0.4.
   1. Model 1 is a better model than Model 2
   2. Model 2 is a better model than Model 1
   3. R² is neither necessary nor sufficient for analysis to be useful

1. Please briefly describe the concept of an outlier and explain some strategies for dealing with outliers.
2. Please explain why residuals need to be squared in process of generating OLS coefficients.
3. OLS does not automatically produce unbiased estimates. Please briefly explain the condition that must be satisfied for OLS to produce unbiased estimates.
4. Please explain the concept of consistency in OLS estimations.
5. Please list and give a short description of the two sources of randomness in the coefficient estimates.
6. Please explain the central limit theorem.