Question

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.

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

1. Is the whole regression model effective in predicting the cost of rent? Use alpha of 0.1.

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

3. 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).

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

Answer 1

EXCEL output: SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.389612547 0.151797937 0.010430927 243.8173523 15 ANOVA Significance F 2 127666.5178 63833.26 1.073786 0.37238823 MS Regression Residual Total 12 713362.8156 59446.9 14 841029.3333 Coefficients Standard Error tstat P-value Lower 95% U per 95% 810.0338491122.4531298 6.615052 2.48E-05 543.2313992 1076.836299 0.270582898 0.188338838 1.436681 0.176365 -0.139772179 0.680937974 Intercept 2018 Population 2010 Median Income-0.1192133310.972308841 -0.12261 0.904447 2.237692306 1.999265644 Since p-value 0.3724) a 0.10), then do not reject the null hypothesis ince p -value

Therefore, the whole regression model is not effective in predicting the cost of rent. The multiple regression equation is Monthly Rent 810.0334+(02706)2018 Population(-0.1192)2010Median Income The estiamted value of the intercept is 810.0334. Interpretation of intercept: The estimated monthly rent is increased by $810.0334 when the 2018 population and 2010 median income does not invest.

The value ofthe estimated slope for the variable "Income" is -0.1192. The monthly rent is decreased by S119.2 when the 2010 median income is increased by 1 thousand dollars, holding 2018 population as constant.