The Brief Case in Chapter 4 introduced the Cost of Living dataset that contains an estimate of the cost of living for 322 cities worldwide in 2013. In addition to the overall Cost of Living Index are: the Rent Index, Groceries Index, Restaurant Index, and the Local Purchasing Power Index, which measures the relative purchasing power of buying goods and services in a city compared to the average wage in that city. Can we reconstruct the overall Cost of Living Index from the four component indices? Here is some multiple regression output:

Assuming that the assumptions and conditions for this model are satisfied,
a) What might you recommend as a next step for developing a regression model? Why? The researcher looking at this problem has proposed the following model:

b) What are the advantages of this model compared to the previous model with four predictors?
c) Why did the researcher remove the Rent Index from the model?
d) Do you think the model with three predictors is better? Explain briefly.

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Dependent variable s: CPI R-squared-97.34% R-squared (adjusted)-97.30% s 4.562 with 322 5 317 degrees of freedom Variable Intercept Rent Inde:x Groceries Index 0.526519 0.020862 25.238 <0.0001 Restaurant Index 0.418352 0.015459 27.063 <0.0001 Local Purchasing Coeff SE(Coeff) t-ratio P-value 12.756575 0.771592 16.533 <0.0001 0.024611 0.019650 1.252 0.2113 Power Index0.017699 0.0079012.240 0.0258 Dependent variable is: CPI R-squared-97.32% R-squared (adjusted)-97.30% 4.566 with 322 4 318 degrees of freedorm Variable (Intercept) 12.513871 0.747530 16.740 <0.0001 Groceries Coeff SE(Coeff) t-ratio P-value 0.537981 0.018764 28.671 <0.0001 Index Index Purchasing0.017215 0.007899 2.179 0.030 Restaurant 0.420932 0.015335 27.450 0.0001 Local Power Index