Basic Estimating

Basic Estimating

Thomas and Maurice (2011) argue that a “Regression analysis uses data on economic variables to determine a mathematical equation that describes the relation between the economic variables. Regression analysis involves both the estimation of parameter values and the testing for statistical significance” (page 121). Thomas and Maurice (2011) further describe regression analysis as a “technique used to determine the mathematical relation between a dependent variable and one or more explanatory variables. The explanatory variables are the economic variables that are thought to affect the value of the dependent variable” (page 121).

A linear regression is generally written in the form Y = aX + b, where Y represents the dependent variable, a represents slope (the rate of change in Y as X changes), and b is the intercept parameter because it gives the value of Y at the point where the regression line crosses the Y-axis (that is, at the point where X = 0). In this problem, the corresponding linear regression is E = a + bN, where E represents total annual earnings of the motion picture industry, N represents the number of tickets that are sold in December (950,000), a is the parameter estimate 25,042,000, and b is the estimate 32.31.

Using E = a + bN,

E = 25,042,000 + 32.31 * 950,000

So, E = 55,736,500

Hence, the total annual earnings of the motion picture industry are estimated to be $55,736,500. Since the earnings for December are estimated at $48,000,000, this means that approximately 86% of the industry’s annual earnings will be generated from the earnings during the month of December.

Thomas and Maurice (2011) suggest that a t-test can be used to check the value of b for statistical significance.

Using t = 32.31 / 8.54

t = 3.78.

Since 3.78 is greater than 2.160 - the critical t-value given by Thomas and Maurice (2011) – then b is statistically significant (page 131).

Given the statistics presented above, I...