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Assignment on Regression Analysis:
Problem No. 35
Page 616
Data set:
Suppose any one
is interested in predicting the prices of a laptop computers based on its various features.
Objective:
Formulate
a multiple regression model that includes all potential explanatory variables and estimate it with the given sample data.
Interpret the estimated regression equation
How well does the estimated model fit the data given in the
file P11_35.XLS
Use the estimated regression equation to predict the price of a laptop computer with the following
features: a 60-megahertz processor, a battery that holds its charge for 240 minutes, 32-megabytes of RAM, a DX chip, a color
monitor, a mouse pointing device, and a 24-hour, toll free customer service hotline.
Selection of Variables:
Here the possible dependent variable is price, as this the variable which we want to predict, on the basis of other features.
The features such as speed, chip type, RAM, charge holding period of battery, monitor type, type of pointing device and availability
of help line are the independent variables. These variables are selected on the basis of scatter plots, and correlation coefficients
between two variables. However looking at the correlation it is observed that the correlation coefficient between price and
speed, chip type, monitor type and pointing device type is high, i.e. more than 0.5 and it is low for RAM, charge holding
period of battery and availability of help line.
Estimation of coefficients:
After analysis of data under noted summary has emerged:
Results of multiple
regression for Price
Summary measures
Multiple R 0.8234
R-Square 0.6780
Adj R-Square 0.5169
StErr of Est 949.1306
ANOVA Table
Source df SS MS F p-value
Explained
7 26549777.4545 3792825.3506 4.2103 0.0107
Unexplained14 12611884.0000 900848.8571
Regression coefficients
Coefficient
Constant 2576.3225
Speed
-58.8411
Charge 7.4865
RAM -18.3404
Chip_Type_DX
2669.9917
Monitor_Type_COLOR 2004.9150
Pointing_Device_MOUSE 428.7334
Help_Line_YES
-453.6128
Testing the Model:
The regression analysis gives the linear relation as:
Price= 2576.32-58.84S+7.49C-18.34R+2669.99D+2004.92M+428.73P-453.61H
For the above analysis, the p value is 0.01,
which is comparatively low. R-Square is 0.678, which is quiet high. The signs associated with the coefficients are also as
expected.
Therefore it can be accepted.
Implementing:
Predicting Price for the specification given
above:
Price: 2576.32-58.84*60+7.49*240-18.34*32+2669.99+2004.92+428.73-453.61
=4906.67
Thus the predicted
price of a laptop computer with the given specifications, should be USD 4906.67, which corresponds with the prices given in
the list.
Also See Sites of Eleanor
and Kelly
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