Week 9

Question 1

What is linear regression?

Answer 1

‘If we change X by one, we’d expect y to change by b’

Question 2

Give and example where transforming data by the natural logarithm may help to facilitate linearity and normality?

Answer 2

Exponentially decreasing graph of life expectancy (y) versus GDP/capita (x).

Becomes life expectancy (y) versus Ln GDP/capita, thus making the line straight (allows a LOBF)

Question 3

Equation when transforming a graph by natural logs, and how it is then interpreted?

Answer 3

ln(y) = a + b(ln(x)) + e

This transformation now means regression coefficients are interpreted as elasticities

Question 4

5 things to infer from this regression equation:

y = a + b1x1 + b2X1^2 + b3X2 + e

Answer 4

Turning point = b1/2b2

Max point: b1 = + and b2 = -
Min point: b1 = - and b2 = +
Exp(inc.): b1 = + and b2 = +
Exp(dec): b1 = - and b2 = -

Question 5

What are interaction variables?

Answer 5

An interaction variable is used when two different x’s have an impact on y if BOTH x’s occur.

Question 6

Example of interaction variables?

Answer 6

Coffee sweetness only occurs if both sugar goes in AND it is stirred - either one of these by them self will not help

Question 7

How is an interaction variable developed?

Answer 7

By multiplying the two interaction variables:

y = a + b1x1 + b2x2 + b3x1x2 + e