Question

Domestic Car Sales

Consider the following multiple regression model of domestic car sales (DCS) where:

DCS = domestic car sales

DCSP = domestic car sales price (in dollars)

PR = prime rate as a percent (i.e., 10% would be entered as 10)

Q2 = quarter 2 dummy variable

Q3 = quarter 3 dummy variable

Q4 = quarter 4 dummy variable

Multiple Regression — Result Formula

DCS = 3,266.66 + ((DCSP) × −0.098297) + ((PR) × −21.17) + ((Q2) × 292.88) + ((Q3) × 149.07) + ((Q4) × −60.25)

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS			df			MS			SEE
Regression		1,834,180.23			5			366,836.05
Error		494,506.47			34			14,544.31			120.60
Total		2,328,686.70			39

Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description	Included in Model			Coefficient			Standard Error			T-test			P-value			F-test			Elasticity			Overall F-test
DCS		Dependent			3,266.66			288.10			11.34			0.00			128.56						25.22
DCSP		Yes			−0.10			0.01			−7.18			0.00			51.50			−0.76
PR		Yes			−21.17			13.77			−1.54			0.13			2.36			−0.11
Q2		Yes			292.88			54.02			5.42			0.00			29.39			0.04
Q3		Yes			149.07			54.11			2.76			0.01			7.59			0.02
Q4		Yes			−60.25			54.22			−1.11			0.27			1.23			−0.01

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	492.41		Durbin Watson	1.62
BIC	494.10		Mean	1,802.86
Mean Absolute Percentage Error (MAPE)	5.30	%	Standard Deviation	244.36
R-Square	78.76	%	Max	2,272.60
Adjusted R-Square	75.64	%	Min	1,421.30
Root Mean Square Error	111.19		Range	851.30

For the domestic car sales regression, the multiple coefficient of determination shows that

Multiple Choice

• 75.64% of the variation in DCS is explained by variation in the independent variables.

• 288.10 will be the error associated with DCS.

• 120.60 is the error associated with the independent variable.

• 3,266.66 will be the most likely value of DCS.

Answer 1

Based on given multiple regression analysis output given,

the coefficient of multiple determination is 78.76%

this indicates that , about 78.76% of total variation in DCS(y ) is explained by the regression model ( means by all independent variables togetherly).

## Answer is

75.64% of the variation in DCS is explained by variation in the independent variables.