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Show that lim inf a_n = lim sup a_n if and only if lim a_n exists

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Solution Summary

This is a proof regarding the existence of a limit.

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Regression model for real estate data

Refer to the data included in the Excel file, which report information on homes sold in the Somewhere, USA, during a recent year. Use the selling price of the home as the dependent variable and determine the regression equation with number of bedrooms, size of the house, whether there is a pool, whether there is an attached garage, distance from the center of the
city, and the number of bathrooms as independent variables.

i) Construct a 95% confidence interval estimate of the population slope between selling price and each of the following variables: number of bedrooms, size in sq. ft., distance to CBD, and number of bathrooms.
j) Compute and interpret the coefficients of partial determination.
k) Predict the selling price of a 2,500 square feet house that has 5 bedrooms, 3 bathrooms,
a 3-car attached garage, no pool, and is at 18 miles from the city center.
l) Rerun the analysis until only significant regression coefficients remain in the analysis. Identify these variables.

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