The American Chamber of Commerce Researchers Association compiles cost-of-living
ID: 3299480 • Letter: T
Question
The American Chamber of Commerce Researchers Association compiles
cost-of-living indexes for selected metropolitan areas. Shown here are cost-of-living
indexes for 25 different cities on five different items for a recent year. Use the data to
develop a multiple regression model to predict the grocery cost-of-living index by the
indexes of housing, utilities, transportation, and healthcare. Discuss the results,
highlighting both the significant and nonsignificant predictors.
CITY GROCERY ITEMS HOUSING UTILITIES TRANSPORTATION HEALTH CARE Albany 108.30 106.80 127.40 4 89.1 107.50 Albuquerque 96.30 105.20 98.80 100.90 102.10 Augusta, GA 96.20 88.80 115.60 102.30 94.00 Austin 98.00 83.90 87.70 97.40 94.90 Baltimore 98.00 83.90 87.70 97.40 94.90 Buffalo 103.10 117.30 127.60 107.80 100.80 Colorado Springs 94.50 88.50 74.60 93.30 102.40 Dallas 105.40 98.90 108.90 110.00 106.80 Denver 91.50 108.30 97.20 105.90 96.20 Des Moines 94.30 95.10 111.40 105.90 114.30 El Paso 102.90 94.60 90.90 104.20 91.40 Indianapolis 96.00 99.70 92.10 102.70 97.40 Jacksonville 96.10 90.40 96.00 106.00 96.10 Los Angeles 89.80 92.40 96.30 95.60 93.60 Louisville 94.60 88.00 79.40 102.40 88.40 Memphis 99.10 211.30 91.10 101.10 85.50 Miami 100.30 123.00 125.60 104.30 137.80 Minneapolis 92.80 112.30 105.20 106.00 107.50 Mobile 99.90 81.10 104.90 102.80 92.20 Nashbille 95.80 107.70 91.60 98.10 90.90 New Orleans 104.00 83.40 122.20 98.20 87.00 Oaklahoma City 98.20 79.40 103.40 97.30 97.10 Phoenix 95.70 98.70 96.30 104.60 115.20Explanation / Answer
Solution: We are using minitab software for multiple regression analysis as follows:
Regression Analysis: GROCERY ITEMS versus HOUSING, UTILITIES, TRANSPORTATION, HEALTH CARE
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 4 194.259 48.5647 3.36 0.032
HOUSING 1 0.895 0.8948 0.06 0.806
UTILITIES 1 73.513 73.5127 5.09 0.037
TRANSPORTATION 1 45.717 45.7168 3.16 0.092
HEALTH CARE 1 13.443 13.4428 0.93 0.348
Error 18 260.216 14.4564
Lack-of-Fit 17 260.216 15.3068 * *
Pure Error 1 0.000 0.0000
Total 22 454.475
Model Summary
S R-sq R-sq(adj) R-sq(pred)
3.80216 42.74% 30.02% 0.00%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 87.32 8.16 10.70 0.000
HOUSING 0.0076 0.0304 0.25 0.806 1.00
UTILITIES 0.1473 0.0653 2.26 0.037 1.43
TRANSPORTATION 0.0195 0.0110 1.78 0.092 1.20
HEALTH CARE -0.0751 0.0778 -0.96 0.348 1.23
Regression Equation
GROCERY ITEMS = 87.32 + 0.0076 HOUSING + 0.1473 UTILITIES + 0.0195 TRANSPORTATION
- 0.0751 HEALTH CARE
Fits and Diagnostics for Unusual Observations
GROCERY
Obs ITEMS Fit Resid Std Resid
1 108.30 108.37 -0.07 -0.44 X
16 99.10 97.90 1.20 0.98 X
Conclusion:(part 1)
From above P values of all predictors we can say that , HOUSING (p value=0.806 ) and HEALTH CARE(p value=0.348) both are not significant because our level of significance is 0.05 and above 2 values are greater than 0.05 so they are not significant. so now we will run the regression analysis without using these predictors as follows:
Regression Analysis: GROCERY ITEMS versus UTILITIES, TRANSPORTATION
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 2 179.898 89.9491 6.55 0.006
UTILITIES 1 60.720 60.7197 4.42 0.048
TRANSPORTATION 1 46.794 46.7937 3.41 0.080
Error 20 274.577 13.7288
Lack-of-Fit 19 274.577 14.4514 * *
Pure Error 1 0.000 0.0000
Total 22 454.475
Model Summary
S R-sq R-sq(adj) R-sq(pred)
3.70524 39.58% 33.54% 0.00%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 83.12 5.56 14.95 0.000
UTILITIES 0.1223 0.0581 2.10 0.048 1.19
TRANSPORTATION 0.0197 0.0107 1.85 0.080 1.19
Regression Equation
GROCERY ITEMS = 83.12 + 0.1223 UTILITIES + 0.0197 TRANSPORTATION
Fits and Diagnostics for Unusual Observations
GROCERY
Obs ITEMS Fit Resid Std Resid
1 108.30 108.35 -0.05 -0.27 X
Conclusion:So from above P values we can say that all the predictors are significant as their p values are less than 0.05. so the regression equation GROCERY ITEMS = 83.12 + 0.1223 UTILITIES + 0.0197 TRANSPORTATION is best for the predictors.
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