Multiple Regression Predicted Values

My data set contains five variables for 96 nations in the world.

Onlinepop Online Population
PC's Number of Personal Computeres
Phones Number of landline phones
Educ Percent of GNP spent on education
GNPPC Gross National Product per capita

Here is correlation matrix on data set:

Assignment was to Regress Onlinepop against PC's, Phones, and Educ and then to regress the predicted values of the dependent variable Onlinepop against the residuals resulting in the following scatterplot in order to detect for heteroskedasticity.
Next based on results of model I was to consider three scenarios. First, triple Education expenditure. Second, double PC's. Third, double Phones. Here are results of model. R square was .98

QUESTION - I don't understand why variable Educ has a negative coefficient. Intuitively, I would expect a positive sign. Can you explain why? Could it be multilcollinearity or is it the heteroskedasticity at work?

See attached file for full problem description.

© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/math/numerical-analysis/multiple-regression-predicted-values-1pm

Solution Preview

...ept 544579.306 613179.8725 0.89 .38
PCs 0.937418021 0.013151766 71.28 2.67337E-82
Phones 0.218685792 0.054724064 3.99 .0001
Educ -187381.0927 132987.9076 -1.40 .1622

QUESTION - I don't understand why variable Educ has a negative coefficient. Intuitively, I would expect a positive sign. Can you explain why? Could it be multilcollinearity or is it the heteroskedasticity at work?

Thanks,

Robin Otto

ANSWER:

First, let's remember that the problem of heteroskedasticity in linear regression involves the assumption or existence of a varying variance of a particular variable over the regressor variable. The more usual case of heteroskedasticity involves a linear regression model such as:

Yi = α + βXi + ei

Where the errors (ei) are heteroskedastic, which could mean, for example, that the variance (σi) of the error term increases with Xi. In such circumstances, the appropriate technique is no longer ...