Question

In: Statistics and Probability

City Cost of Living Index Rent (in City Centre) Monthly Pubic Trans Pass Bottle of Wine...

City Cost of Living Index Rent (in City Centre) Monthly Pubic Trans Pass Bottle of Wine (mid-range) Loaf of Bread Milk
London 88.33 $4,069.99 $173.81 $10.53 $1.23 $4.63
Dublin 87.93 $3,025.83 $144.78 $14.12 $1.37 $4.31
Paris 89.94 $2,701.61 $85.92 $8.24 $1.56 $4.68
Rome 78.19 $2,354.10 $41.20 $7.06 $1.38 $6.82
Amsterdam 85.9 $2,823.28 $105.93 $7.06 $1.33 $4.34
Berlin 71.65 $1,695.77 $95.34 $5.89 $1.24 $3.52
Athens 63.06 $569.12 $35.31 $8.24 $0.80 $5.35
Brussels 82.2 $1,734.75 $57.68 $8.24 $1.66 $4.17
Madrid 66.75 $1,795.10 $64.27 $5.89 $1.04 $3.63
Prague 50.95 $1,240.48 $25.01 $5.46 $0.92 $3.14
Warsaw 45.45 $1,060.06 $30.09 $6.84 $0.69 $2.68
Tokyo 92.94 $2,197.03 $88.77 $17.75 $1.77 $6.46
Sydney 90.78 $3,777.72 $124.55 $14.01 $1.94 $4.43
New York 100 $5,877.45 $121.00 $15.00 $2.93 $3.98
Mumbai 31.74 $1,642.68 $7.66 $10.73 $0.41 $2.93
Vancouver 74.06 $2,937.27 $74.28 $14.38 $2.28 $7.12
Seoul 83.45 $2,370.81 $50.53 $17.57 $2.44 $7.90

You’ll find the 2017 data for 17 cities in the data set Cost of Living. Included are the 2017 cost of living index, cost of a 3-bedroom apartment (per month), price of monthly transportation pass, price of a mid-range bottle of wine, price of a loaf of bread (1 lb.) and the price of a gallon of milk. All prices are in U.S. dollars. Examine the relationship between the overall cost of living and the cost of each of these individual items by using linear regression. Verify the necessary conditions and describe the relationship in as much detail as possible (remember to look at direction, form and strength). Identify any unusual observations (outliers), research and discuss. Based on the linear regressions and your analysis, which item would be the best predictor of the overall cost in these cities? Which would be the worst? Are there any surprising relationships? Describe in detail your analysis, results and conclusions.

Solutions

Expert Solution

Examine the relationship between the overall cost of living and the cost of each of these individual items by using linear regression.

The linear regression between the overall cost of living and Rent (in City Centre) is as follows:

0.495 n   17
r   0.703 k   1
Std. Error   13.684 Dep. Var. Cost of Living Index
ANOVA table
Source SS   df   MS F p-value
Regression 2,749.1946 1   2,749.1946 14.68 .0016
Residual 2,808.6562 15   187.2437
Total 5,557.8509 16  
Regression output confidence interval
variables coefficients std. error    t (df=15) p-value 95% lower 95% upper
Intercept 50.1985
Rent (in City Centre) 0.0103 0.0027 3.832 .0016 0.0046 0.0160

The linear regression equation will be:

Cost of Living Index = 50.1985 + 0.0103*Rent (in City Centre)

This means that for every $1 increase in Rent, the Cost of Living Index will be increased by 0.0103.

The linear regression between the overall cost of living and Monthly Public Trans Pass is as follows:

0.578 n   17
r   0.760 k   1
Std. Error   12.511 Dep. Var. Cost of Living Index
ANOVA table
Source SS   df   MS F p-value
Regression 3,209.9682 1   3,209.9682 20.51 .0004
Residual 2,347.8827 15   156.5255
Total 5,557.8509 16  
Regression output confidence interval
variables coefficients std. error    t (df=15) p-value 95% lower 95% upper
Intercept 51.3466
Monthly Pubic Trans Pass 0.3095 0.0683 4.529 .0004 0.1638 0.4552

The linear regression equation will be:

Cost of Living Index = 51.3466 + 0.3095*Monthly Public Trans Pass

This means that for every $1 increase in Monthly Public Trans Pass, the Cost of Living Index will be increased by 0.3095.

The linear regression between the overall cost of living and Bottle of Wine (mid-range) is as follows:

0.231 n   17
r   0.481 k   1
Std. Error   16.879 Dep. Var. Cost of Living Index
ANOVA table
Source SS   df   MS F p-value
Regression 1,284.1123 1   1,284.1123 4.51 .0508
Residual 4,273.7386 15   284.9159
Total 5,557.8509 16  
Regression output confidence interval
variables coefficients std. error    t (df=15) p-value 95% lower 95% upper
Intercept 53.3288
Bottle of Wine (mid-range) 2.1283 1.0025 2.123 .0508 -0.0085 4.2651

The linear regression equation will be:

Cost of Living Index = 53.3288 + 2.1283*Bottle of Wine (mid-range)

This means that for every $1 increase in Bottle of Wine (mid-range), the Cost of Living Index will be increased by 2.1283.

The linear regression between the overall cost of living and the Loaf of Bread is as follows:

0.568 n   17
r   0.754 k   1
Std. Error   12.652 Dep. Var. Cost of Living Index
ANOVA table
Source SS   df   MS F p-value
Regression 3,156.8757 1   3,156.8757 19.72 .0005
Residual 2,400.9752 15   160.0650
Total 5,557.8509 16  
Regression output confidence interval
variables coefficients std. error    t (df=15) p-value 95% lower 95% upper
Intercept 44.0470
Loaf of Bread 21.3894 4.8163 4.441 .0005 11.1236 31.6552

The linear regression equation will be:

Cost of Living Index = 44.0470 + 21.3894*Loaf of Bread

This means that for every $1 increase in Loaf of Bread, the Cost of Living Index will be increased by 21.3894.

The linear regression between the overall cost of living and Milk is as follows:

0.203 n   17
r   0.450 k   1
Std. Error   17.185 Dep. Var. Cost of Living Index
ANOVA table
Source SS   df   MS F p-value
Regression 1,127.9392 1   1,127.9392 3.82 .0696
Residual 4,429.9117 15   295.3274
Total 5,557.8509 16  
Regression output confidence interval
variables coefficients std. error    t (df=15) p-value 95% lower 95% upper
Intercept 49.6351
Milk 5.4879 2.8081 1.954 .0696 -0.4975 11.4732

The linear regression equation will be:

Cost of Living Index = 49.6351 + 5.4879*Milk

This means that for every $1 increase in Milk, the Cost of Living Index will be increased by 5.4879.

Based on the linear regressions and your analysis, which item would be the best predictor of the overall cost in these cities? Which would be the worst? Are there any surprising relationships?

The loaf of bread would be the best predictor of the overall cost in these cities.

Rent (in City Centre) would be the worst predictor of the overall cost in these cities.

The surprising relationship is between the overall cost of living and Monthly Public Trans Pass.


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