3. Testing Hypotheses about Single Coefficients

Question 1

Null hypotheses

Answer 1

The original hypothesis which we are challenging

Question 2

Alternative hypothesis

Answer 2

The hypothesis which we are instead putting forward

Question 3

What do we need to draw perfect statistical inferences?

Answer 3

We need to know everything about the sampling distribution of our estimators

Question 4

When do we know everything about the sampling distribution of our estimators?

Answer 4

If we know their means and variances and the distribution is normal

Question 5

What is MLR6?

Answer 5

The population disturbances (u) are independent of the explanatory variables and are normally distributed with zero means and variance ó^2

Question 6

When do we reject Ho?

Answer 6

When the probability of getting the estimate is less than the significance level

Question 7

Why do we use the t distribution?

Answer 7

Because it takes into account the fact we have estimated ó^2 and it takes into account how much info we used

Question 8

How many degrees of freedom do we get?

Answer 8

n-k-1

Question 9

When can we draw inferences about causal relationships from OLS estimates?

Answer 9

When the CLM assumptions are valid

Question 10

P value

Answer 10

The exact significance level at which an estimate ceases to be significantly significant

Question 11

In a two sided test with 5% sig level, if the p value is 3% is there sufficient evidence to reject Ho?

Answer 11

Yes because the p value is split each end so it will actually be in the 1.5th percentile at each end

Question 12

Type 1 error

Answer 12

When we reject a true null, the probability of this happening is equal to the significance level

Question 13

Type 2 error

Answer 13

When we fail to reject a false null

Question 14

What is the power of a test

Answer 14

Power=1- prob(type 2 error)

Question 15

How are type 1 and type 2 errors related?

Answer 15

They are inversely related

Question 16

Confidence intervals

Answer 16

A range of values where a certain % of values will fall. E.g for a 5% significance level 95% of values will fall here

Question 17

SSE

Answer 17

Explained sum of squares. Measures the variation in ŷi, I.e the variation in yi that is explained by the model

Question 18

SSR

Answer 18

Residual sum of squares. Measures the variation in ûi, I.e. the variation in yi that is unexplained

Question 19

Equation for R^2

Answer 19

R^2= SSE/SST= 1-SSR/SST

Question 20

What is R^2?

Answer 20

It is the ratio of the explained variation to the total variation. Written in other words it is the fraction of the sample variation in y that is explained by all of x

Question 21

Evaluate the effectiveness of R^2

Answer 21

• a higher R^2 shows a better fit of the model to the data
• can be used to compare models with the same dependent variable
• adding an extra variable will increase R^2 even if it doesn’t improve the model

Question 22

Adjusted R^2 formula

Answer 22

Adjusted R^2= 1-((1-R^2) x (n-1)/(n-k-1)

Question 23

Evaluate the adjusted R^2

Answer 23

• adjusted R^2< R^2
• as k increases, the size of the adjustment increases
• it is used to compare models with different k
• the adjustment is arbitrary and the value can rise when a statistically insignificant regressor is added to the model