Bi-variate Analysis

Question 1

Bi-variate relationship

Answer 1

Evaluate relationship between 2 variables

Question 2

Line of best fit

Answer 2

Distance between line and scatterplot points should be as small as possible

Question 3

^y = ^B(0)+^B(1)x+U

Answer 3

expected value of y equals the estimated slope time x plus the estimated y-intercept, plus the error (u)

Question 4

Residuals

Answer 4

• difference between actual and estimated values

- minimizing sum of squared residuals suggests actual and estimated are close

Question 5

U

Answer 5

omitted variables that impact y

Question 6

Regression

Answer 6

At the end of the day this is an estimate / prediction

Question 7

B(0)

Answer 7

estimated y-intercept, predicted value of y when x = 0

Question 8

B(1)

Answer 8

estimated slope, predicted change in y, when x changes by 1 unit

Question 9

Correlation Coefficient

Answer 9

measures how variances move / tightness of relationship
covariance / variance(x)*variance(y)
always between -1 and 1

Question 10

Derivative

Answer 10

taking derivative then setting formula equal to 0 will minimize sum of least squares

Question 11

Percentage Point

Answer 11

• A % change relative to what you had before

- of a share

Question 12

covariance(x,u)

Answer 12

• Measure of if x is correlated with any omitted variables that influence the regression
• cov(x,u) must = 0 or regression is biased
• biased because we can’t establish casual effect, if y has a relationship w another variable

Question 13

R-squared

Answer 13

AKA coefficient of determination, measures if line through a scatter is a good fit
The percent of variation in y that is explained by the model - what % of the variation in y are we getting
The higher the better, but only valuable if we want to precisely predict y
No effect with a higher sample size, but adding new regressors (k) will increase r-squared

Question 14

Ceterus Paribus

Answer 14

-Rule out the possibility of other factors changing casual relationship, by holding other factors affecting dependent variable constant

Question 15

E[^B(1)] formula

Answer 15

• β1 + covariance(x,u) / variance(x)
• bias will depend on whether or not cov(x,u) will be positive or not
• if it is positive and ignored, then B1 is most likely biased down and vice-versa
• for the expected value of B1-hat to equal B1, the cov(x,u) must be 0

Question 16

4 Conditions for OLS to Yield Unbiased Estimator

Answer 16

1. random sample
2. y and x relationship must be linear in parameters
3. variation in x
4. cov(x,u) = 0

These four conditions being met, means that E(B1^) = B1

Question 17

P-value Approach

Answer 17

Alternative to finding t-critical

Probability of obtaining ^B(1) or a more extreme slope estimate

Question 18

P-value final answer

Answer 18

p-value > sig-level = |t-actual| < t-critical

p-value < sig-level = |t-actual|>t-critical

Question 19

Statistical Significance

Answer 19

Rejecting null hypothesis that slope = 0 means x has some level of non-zero effect on y

Question 20

cov(x,u) = 0

Answer 20

NO correlation between x and all the other variables that affect y

Question 21

Interpreting slope / y-int

Answer 21

Don’t forget this are predicted / estimated values and impacts

Question 22

Omitted Variables Bias (^B1)

Answer 22

if cox(x,u) > 0 - biased down because you are ignoring a positive correlation, and the estimated value of ^B1 is bigger b/c we are ignoring the positive correlation

if cov(x,u) < 0 - biased up because ignoring the negative correlation would be the expected value of ^B1 is likely smaller than what we thought

Question 23

Linear in Parameters

Answer 23

In order for us to run a regression the relationship between two variables, has to be a straight-line

Question 24

Variation in X

Answer 24

To tell the relationship between x and y, you need different x-values, no vertical line

No variation in x would make var(x) = 0

Question 25

Homoscedastic Assumption

Answer 25

• v.var(u|x) = sigma-squared, if this condition of constant variance holds, we can estimate variance on ^B1
• needs to hold to get BLUE
• spread is the same as x-changes

Question 26

v.var(u|x)

Answer 26

variance of u conditional on x

Question 27

Multivariate Bias Conditions

Answer 27

1. random sample
2. linear in-parameters
3. no perfect correlation between variables
4. cov(x,u) = 0

perfect correlation only occurs if you include the same variable 2x or if you have two variables that sum to another variable.