Regression Models for Desklib Online Library

Regression Models
Regression Model Assignment
Student’s Name
Institution Affiliation

Regression Models
I. Descriptive statistics of Sale Price, Length and Weight
According to Goos &Meintrup (2015), descriptive statistics includes the measure of
central tendency and measure of dispersion. The measures of central tendency are
mean, median and mode, while dispersion is measured using variance, standard
deviation, maximum and minimum, range, quartiles, and interquartile range. The
descriptive statistics of the sales price, length and weight of the car were determined
on Microsoft Excel and results are shown below.
Statistics
Sales Price Length Weight
Central Tendency
Mean 39699 469 1562
Median 34842 471 1545
Mode 29424 449 1716
Dispersion
Variance 387164687 1000 96985
Standard Deviation 19677 32 311
Maximum 126908 557 2575
Minimum 13042 366 916
Range 113866 192 1660
Quartile(Q3) 47913 491 1733
Quartile(Q1) 26792 449 1363
Inter-quartile Range 21121 42 371

Regression Models
The mean is greater than the median, which is greater than the mode for the three
variables. This indicates that the distributions for the three are positively skewed
(Sharma 2007; Data& Using Descriptive Statistics Bartz 1988). The variances and
standard deviations of the three variables are very high. Higher variance and standard
is an indicator of much-dispersed data points from the mean (Bernstein& Bernstein
1998). According to Brase& Brase (2011), a big range indicates a greater dispersion
of data points, whereas a small range shows a less dispersion. Comparing the three
variables, sales price has the biggest range and interquartile range, what makes its
data to have the greatest dispersion among the three.
II. Estimation of a simple regression model of the Sale price on Length,
Sale Price= β0 + β1 length+ u
The values of β0 and β1 were determine using Microsoft Excel, regression analysis.
The results are shown below.
SUMMARY OUTPUT
Regression Statistics

Regression Models
Multiple R 0.330323
R Square 0.109113
Adjusted R
Square 0.105535
Standard
Error 18609.28
Observations 251
ANOVA
df SS MS F
Significance
F
Regression 1 1.06E+10 1.06E+10 30.49674 8.4E-08
Residual 249 8.62E+10 3.46E+08
Total 250 9.68E+10
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
99.0%
Upper
99.0%
Intercept -56711.5 17497.65 -3.24109 0.001353 -91173.8 -22249.3 -102131 -11292.6
Length 205.5067 37.2134 5.522385 8.4E-08 132.2136 278.7999 108.9112 302.1022
From the above results, the simple regression model for estimate sale price is given
^Sale price=−55711.50+205.5067 length
¿ 205.5067 length−55711.50
III. Estimation of a simple regression model of the Sale price on
Length with the log-log specification.
log Sale Price=β0+ β1 log length+u
β0∧β1 ,are estimated on Excel, the results are shown below
SUMMARY OUTPUT
Regression Statistics