Question

In: Statistics and Probability

Suppose we wish to build a multiple regression model to predict the cost of rent (dollars)...

Suppose we wish to build a multiple regression model to predict the cost of rent (dollars) in a city based on population (thousands of people), and income (thousands of dollars). Use the alpha level of 0.05.

A. Is the whole regression model effective in predicting the cost of rent? Use alpha of 0.1. Make sure to show which values you use to make the decision.

B. Write down the multiple regression equation using actual names of IVs and DVs.

C. What is the value of the estimated intercept? Interpret the value in terms of rent (dollars) based on population (thousands of people), and income (thousands of dollars).

D. What is the values of the estimated slope for the variable “Income”? Interpret the value in terms of actual names of IVs and the DV.

E. What is the values of the estimated slope for the variable “Population”? Interpret the value in terms of actual names of IVs and the DV.

F. Does Income significantly influence the Rent at the alpha level of 0.01? Make sure to show which values you use to make the decision.

G. Does Population significantly influence the Rent at the alpha level of 0.01? Make sure to show which values you use to make the decision.

Data:

City Monthly Rent ($) 2018 Population (Thousands) 2010 Median Income (Thousands of Dollars)
Denver, CO 998 586.158 45.438
Birmingham, AL 711 212.237 301.704
San Diego, CA 1414 1307.402 61.962
Gainesville, FL 741 124.354 28.653
Winston-Salem, NC 750 239.617 41.979
Memphis, TN 819 646.889 36.535
Austin, TX 900 790.39 51.236
Seattle, WA 1219 618.66 58.99
Richmond, VA 735 204.214 37.735
Charleston, SC 812 120.083 47.799
College Park, MD 1407 30.413 66.9
Savannah, GA 789 136.286 32.778
Minneapolis, MN 988 394.578 45.625
Detroit, MI 650 713.777 29.447
Baton Rouge, LA 827 229.493 35.436

Solutions

Expert Solution

I used R software to solve this problem.

R code

orchestra answered 2 years ago
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