Lecture 2 (Chapter 3 in book)

Question 1

Regression - define regression and describe how it differs from correlation

Answer 1

Regression describes and evaluates the relationship between a given variable (dependent variable) and one or more other variables (independent variable(s))

Denote dependent (y) and independents (x1, x2, x3… Xk)

With correlation, we are treating X and Y in a completely symmetrical way. I.e. X could cause Y and Y could cause X

In regression we treat X and Y very differently. We assume that changes in X is the changes in Y. Y is said to be random or stochastic.

Question 2

Describe the steps of a simple regression

Answer 2

Say k = 1 (y depends on only one X variable)

Y = returns of fund FF over time.

X = Excess return of the market

We have some intuition that the Beta on this fund is positive and we therefore want to find whether there is a relationship between X and Y.

Step 1:
- Scatter plot

Step 2:
-Finding a line of best fit:
y = a + Bx(t) + ut
(we add ut as the error term as otherwise entirely deterministic

Question 3

Statistical inference:

Yt = 20.3 + 0.5091Xt

(14.38) (0.2561)

Please outline step for step what you would do to test for H0: beta = 0.5

Answer 3

H0: beta = 0.5
H1: beta not 0.5

Answer pg.18 on Lesson 2

Question 4

Please answer:
In the past you made 70% of your basketball shots. Today you made 75% out of 30 shots. You want to test if this is your new mean or if it is just a lucky day.

Answer 4

Steps involved in doing test of significance are:

H0: Shots = 0.70 H1: Shots > 0.70

Past average (pop. mean μ) = 0.70

Sample mean xˉ = 0.75

Number of shots N = 30

Calculate Standard Error (Typically given)

SE = SqRoot(μ x (1-μ)/n) = SqRoot(0.70*0.30)/30) = 0.08367

t-statistic = (xˉ - μ)/SE = (0.75-0.70)/0.08367 = 0.59761

*Compare t-statistic to critical t-value.
Let’s assume 5% level of significance (α= 0.05)

Compare to a one tailed test with 0.05 at n-1 (29) degrees of freedom = 1.699

Because 0.59761 is lower than 1.699 we cannot reject the null hypothesis –> i.e. there is not enough evidence to conclude that your shooting has significantly improved

Question 5

Please explain Type I and Type II errors in the null hypothesis

Answer 5

Type I: The rejection of the null hypothesis when it is actually true.

Type II: The failure to reject the null hypothesis when it is false

Question 6

If we reduce the size of the significance level do we reduce or increase the chance of a type I error?

Answer 6

We decrease it because we lower the chance of rejecting the null hypothesis because we impose more strict criterion for rejection, the null is less likely to be rejected, thus minimising Type I error.