Quantitative Methods

Question 1

error term (residual)

Answer 1

The portion of the dependent variable that can’t be explained by the independent variable

Question 2

dependent variable

Answer 2

Y - the variable we’re seeking to explain

Question 3

independent variable

Answer 3

X - the explanatory variable

Question 4

Cross-sectional

Answer 4

many observations on X & Y for the same time period

Question 5

Time series

Answer 5

many observations on Y (and sometimes X) from different time periods

Question 6

Assumptions underlying linear regression

Answer 6

1. The relationship between X & Yis linear in the parameters b0 and b1 (meaning both are raised to the 1st power only and neither is multiplied/divided by another regression parameter)
2. X is not necessarily random
3. Expected value of error terms = 0
4. Variance of error terms is the same for all observations
5. Error term is uncorrelated across observations (in other words, no serial correlation) -> this is needed to correctly estimate the variances of b0 and b1
6. Error term is normally distributed

Assumptions 2/3 -> ensure that correct estimates of b0 and b1 are produced

Assumption 4/5/6 -> determine the correct distribution of b0 & b1 so we can test the values of the coefficients

Question 7

Standard error of estimate

Answer 7

Measures the standard deviation of error term

SEE = (SSE/n-2)^0.5 or (MSE)^0.5

Question 8

Coefficient of determination

Answer 8

Measures the faction of the total variation in the dependent variable that’s explained by the independent variable

R^2 = EXPLAINED VARIATION/TOTAL VARIATION

Question 9

Confidence interval for a regression coefficient

Answer 9

An interval of values that is believed to incl. the true parameter value of b1 w/a given degree of confidence

b1 +/- (critical t value) * (standard error of estimate of b1)

Question 10

Hypothesis testing

Answer 10

t = (^b1-b1)/(std error of estimated regression coefficient)

if |t test statistic| > |critical t value| -> reject H0 -> conclude statistical significance

Usually H0: regression coefficient = 0

Question 11

P-value

Answer 11

Smallest level of significance at which H0 can be rejected (2-sided test)

If p-value < significance level -> reject H0 -> conclude statistical significance

Question 12

ANOVA

Answer 12

ANalysis Of VAriance - determine the usefulness of the independent variables in explaining the variance in the dependent variable

SSE = sum of squared errors (unexplained)
RSS = regression sum of squares (explained) -> total variation in Y that's explained by the regression equation

TSS = SSE + RSS

Question 13

Limitations of regression analysis

Answer 13

• Regression relations can change over time (Parameter instability)
• Public knowledge may negate usefulness of analysis
• Output depending on regression assumptions -> Tests can be performed on error terms

Question 14

Multiple regression

Answer 14

Difference from linear regression is that now you have more than 1 independent variable

e. g. Y = -23 + 0.3X1 - 0.225X2
0. 3 represents the expected effect on Y of a 1-unit increase X1 after removing the part of X1 that is correlated w/X2

If X1 and X2 are uncorrelated, then a regression w/just X1 would have the same coefficient