Managerial Economics

Exercise 1 (Simple Linear Regression):

(a)Plot the data.

[pic 1]

(b) Determine the estimated regression line. Give an economic interpretation of the

estimated slope (b) coefficient.

Estimated regression line:

y=5.25x+30.18

Economic interpretation of the estimated slope coefficient:

                Slope coefficient represents change in sales due to one additional unit of distance.

                Sales increases by £5250 by every additional kilometer of distance.

(c) Determine if distance is a statistically significant variable in estimating sales.

[pic 2]

The P-value of 0.25% depicts the statistical significance of the variable, distance.

(d) Calculate the coefficient of determination.

        R Square=0.52

[pic 3]

(e) Perform an F-test of the overall significance of the results.

[pic 4]

(f) Construct an approximate 95% prediction interval for the sales if the nearest competitor

locates at a distance of 9.6 Km.
        95% confidence interval is derived from y’+/-2Se

        y’=80.58, Se=13.19

[y’-2Se, y’+2Se]

        = [80.58-2Se, 80.58+2Se]

        = [54.2, 106.96]

Exercise 2 (Multiple Linear Regression): Ransome Airlines developed the following

(a) Which of the independent variables (if any) appear to be statistically significant (at

the 0.05 level) in explaining the demand for tickets?

Both variables are significant in explaining the demand for tickets.

        b1= -0.42 b2= 0.27

df= # of observations – (# of independent variables + 1) = 42

t-value= 1.68 (derived from the t-value table)

        t-statistic for b1= -13.13

 [pic 5]

-0.42 – 0/ 0.032

=-13.13 < 1.68

Thus, rejects the null hypothesis of no relation between demand and price. [pic 6]

        t-statistic for b2= 3.86

        [pic 7]

        0.27 – 0/ 0.07

= 3.86 > 1.68

Thus, rejects the null hypothesis of no relation between advertising and price. [pic 8]

Negative linear relationship exists between demand and tickets price.

        Positive linear relationship exists between demand and advertising expense.

(b) What proportion of the total variation in sales is explained by the regression equation?