Question

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.

Answer 1

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:

	r²	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:

	r²	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:

	r²	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:

	r²	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:

	r²	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.