Price Weight Specficiation 1 reg price weight ----------------------------------

ID: 3321165 • Letter: P

Question

Price Weight

Specficiation 1

reg price weight

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price | Coef. Std. Err. t P>|t| [95% Conf. Interval]

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weight | 2.044063 .3768341 5.42 0.000 1.292857 2.795268

_cons | -6.707353 1174.43 -0.01 0.995 -2347.89 2334.475

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Specification 2

. gen weight2 = weight^2

. reg price weight weight2

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price | Coef. Std. Err. t P>|t| [95% Conf. Interval]

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weight | -7.273097 2.691747 -2.70 0.009 -12.64029 -1.905906

weight2 | .0015142 .0004337 3.49 0.001 .0006494 .002379

_cons | 13418.8 3997.822 3.36 0.001 5447.372 21390.23

1.Write out the model estimated in each specification.

2.The R-square of the first specification is 0.29. The R-square of the second specification is 0.39.

What’s the story here?

The regression equation is formed using the coefficients as

model 1

price = -6.707 + 2.044*weight

for model 2

price = 13418.8 + 0.0015142*weight2 -7.273*weight

The r2 value is called coefficient of determination

It explains the variation that is explained by the model , higher the value better the model.
The value of r2 can range from 0 to 1

the r2 for first model is 0.29 , this means that model is able to explain 29% variation in price due to independent variables

the r2 for second model is 0.39 , this means that model is able to explain 39% variation in price due to independent variables

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