Question

A firm is experiencing theft problems at its warehouse. A consultant to the firm believes that the dollar loss from theft each week (T) depends on the number of security guards (G) and on the unemployment rate in the county where the warehouse is located (U measured as a percent). In order to test this hypothesis, the consultant estimated the regression equation T = a + bG + cU and obtained the following results:

Dependent Variable	T	R-Square	F-Ratio	P-Value on F
Observation	27	0.7798	42.38	0.0001
Variable	Parameter Estimate	Standard Error	T-Ratio	P-Value
Intercept	5150.43	1740.72	2.96	0.0068
G	-480	130.66	-3.68	0.0012
U	211.0	75.0	2.81	0.0096

The value of R² tells us that
a. 0.7793% of the total variation in G is explained by the regression equation.
b. 77.98% of the total variation in T is explained by the regression equation.
c. 42.38% of the total variation in G, U, and R is explained by the regression equation.
d. 0.0001% of the total variation in P, ln Q, and R is explained by the regression equation.

	a.	..
	b.	..
	c.	..
	d.	..

Answer 1

Solution:

R-squared tells how well the regression model is, that is, how well the independent variables together, explain the dependent variable. In this sense, it is a measure of goodness of fit, that how well the regression line fits the model in hand.

In the given question, the dependent variable is dollar loss from theft, denoted by T. Independent variables are number of guards, G and unemployment rate, U. The regression equation includes G and U, so here T-square tells how well G and U explains the variation in T.

With value of R-squared = 0.7798 or 77.98% (since the value always lie within range of -1 and 1, denoting 100%), it means that 77.98% of variation in T is explained by G and U, that is the regression equation. So, correct option is (B).