# Using Ordinary Least Square: Model Coefficients And The Price Of The Market

Submitted By Menghan-LI
Words: 6081
Pages: 25

Content

Part A 2
 Question 1 2
 Question 2 3
 Question 3 4
 Question 4 6
 Question 5 8
 Question 6 9
Part B 13
 Question7 13
 Question 8 16
 Question 9 19
Part C 21
 Question 10 21
 Question 11 25
 Question 12 35

Part A
Introduction
Given the background that motorcycles registration growth faster in last year, the purpose the subject is to study different market differentiation among different brands. The variables are given and the data were collected in order to work out the relationship among variables and the price of the motorcycles.

Question 1
Using Ordinary Least Square (OLS) method estimates the regression model. The below is the estimating model to help with model estimation (hint: use the estimated coefficients to write the regression equation based on the following model).
Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients t Sig.

B
Std. Error
Beta

1
(Constant)
-438.487
775.027

-.566
.573

Bore
.508
18.895
.005
.027
.979

Displacement
7.552
2.187
.567
3.453
.001

Clearance
259.345
44.955
.360
5.769
.000

Stroke
946.424
224.885
.216
4.208
.000

Wheelbase
-11.057
22.872
-.039
-.483
.630
a. Dependent Variable: MSRP
Figure A-1
The following formula is to estimate the regression model:
MSRP = β0 + β1 BORE + β2 DISPLACEMENT + β3 CLEARANCE
+ β4 ENGINE STROKES + β5 WHEELBASE + ε

Note:
a) β0 is constant, which means as a decisive factor of price, it does not change when the regressors or the random factor change.
b) ε is the random error, we assume that the random error with a mean equal to 0 and constant variance

As graph shows above, β0 (constant)=-438.487, β1 (Bore)=0.508, β2 (DISPLACEMENT)=7.552, β3 (CLEARANCE)=259.345, β4 (ENGINE STROKES)=946.424, β5 (WHEELBASE)=-11.057

Therefore, the outcome is:
MSRP=-438.487+0.508 BORE+7.552 DISPLACEMENT+259.345 CLEARANCE+946.424 ENGINE STROKES-11.057 WHEELBASE

Question 2
What are the a priori signs of the coefficients based on your experience or theories and are they the same as the signs of the estimated coefficients from the model in the SPSS output?
The priori signs:
Based on the experience of real life,

Bore: β1 (coefficient of Bore) should be positive. Because the larger the bore is, the higher price of the motorcycle would be.

Displacement: β2 (coefficient of displacement) should be positive. Because the larger displacement is, the higher cost of the motorcycle would be.

Clearance: β3 (coefficient of clearance) should be positive. Because the larger clearance is, the higher cost of the motorcycle would be.

Stroke: β4 (coefficient of stroke) should be positive. Because the larger stroke is, the higher cost of the motorcycle would be.

Wheelbase: β5 (coefficient of wheelbase) should be positive. Because the larger wheelbase is, the higher cost of the motorcycle would be.

As Figure A-1 shows, the coefficient of priori signs are all positive besides Wheelbase which means that signs of the estimated coefficients of bore, displacement, clearance, stroke are the same as the a priori signs. However, the coefficient of priori sign for wheelbase is different.

In conclusion, priori signs of the coefficients based on our experience or theories are the same as the signs of the estimated coefficients besides wheelbase from the model in the Figure A-1. Because a priori signs do agree with those in the estimated model, the regression may be worthwhile.

Question 3
Interpret the estimated coefficients of the model and check whether these coefficients are significant
Interpretation:
According to the equation above,
MSRP=-438.487+0.508 BORE+7.552 DISPLACEMENT+259.345 CLEARANCE+946.424 ENGINE STROKES-11.057 WHEELBASE

The price of motorcycle increases by 0.508, on average, for the each 1 inch increase in Bore.
 The price of motorcycle increases by 7.552, on average, for the each 1 cu inch increase in Displacement.
The price of motorcycle increases by 259.345, on average, for the each 1 inch increase