Question

Question 1

A consulting company looked at the effect of company size (X), measured in terms of oper-

ating costs, on profits (Y). They looked at 30 different companies of various sizes, and found

the following results:

∑Xi = 1200

∑Yi = 450

Sample Correlation coefficient between X any Y,

Rxy= 0.45

Sample covariance of x and y is 5

Sample variance of y is 6

Do the following:

A: Given the information above, calculate the sample variance of X

B: Estimate the model, finding B hat 0 and b hat 1

C: Interpret the meaning of B hat 1 (B^1)

in words.

D: Does this model violate the 2nd OLS assumption from the textbook? Why or why not?

(The assumption states that the variance of

e

, the error term, is the same for all x’s). Your

answer should be based on intuitions, not on formulae.

Answer 1

(A)

Given:

Substituting values, we get:

So,

s_X = 4.5260

So,

Variance of X is given by:

s²_X = 20.4847

(B)

(i) Slope = b₁ is given by:

= 1200/30 = 40

= 450/30 = 15

Intercept = b₀ is given by:

    = 15 - (0.2435 X 40)

   = 5.2583

(C)
Interpretation of b₁ , Slope = 0.2435

If the company size increases by 1 unit, we predict the profit will increase by 0.2435.

(D)

The variance of error term is the same for all values of X. This condition is called homoscedasticity. It means that when we plot the individual error against the predicted value, the variance of the error predtcted value should be constant. Scatter plot is used for testing the same.