Question

Using the table below

NATIONALITY	TOTAL PERSONS	TOT_SPEND	DAYS	FIRST-TIME
GERMAN	4	1095	9	yes
ITALIAN	5	867	8	no
FRENCH	4	689	10	no
BRITISH	5	876	16	yes
FRENCH	5	1280	17	yes
FRENCH	4	755	10	no
FRENCH	3	375	9	no
BRITISH	4	275	4	no
ITALIAN	5	1166	11	yes
GERMAN	4	1741	13	yes
BRITISH	4	302	5	yes
BRITISH	4	423	11	no
BRITISH	4	659	7	no
BRITISH	3	358	10	no
ITALIAN	4	785	9	yes
BRITISH	5	1046	15	no
BRITISH	4	373	5	no
GERMAN	5	517	6	yes
ITALIAN	3	486	12	yes
BRITISH	4	357	6	no
ITALIAN	5	436	5	yes
FRENCH	3	800	13	yes
BRITISH	4	613	7	no
GERMAN	3	688	11	yes
BRITISH	3	433	7	no
BRITISH	3	239	6	yes
BRITISH	4	464	8	no
FRENCH	4	923	14	no
BRITISH	3	187	5	no
FRENCH	3	357	12	no

Suppose you want to use the non-numeric variables “Nationality” and “First time visit”, as explanatory variables in a regression model regarding “Total spending”

i. How many “dummy variables” and which ones do you need to create?

ii. State a regression model of Total spending using as explanatory variables “PersonDays” (new variable computes as Total Persons X Days), “Nationality”, and “First time visit”. You believe that “Nationality” affects the slope coefficient of “PersonsDays”, while “First time visit” affects the intercept.

iii. Run the regression and state the estimated model for each Nationality distinguishing between first time and repeated visitors.

iv. Which coefficients are statistically significant?

v. Run the model after you remove the non-significant coefficients. Compare with the model in (ii) and comment

Answer 1

i. How many “dummy variables” and which ones do you need to create?

2

ii. State a regression model of Total spending using as explanatory variables “PersonDays” (new variable computes as Total Persons X Days), “Nationality”, and “First time visit”. You believe that “Nationality” affects the slope coefficient of “PersonsDays”, while “First time visit” affects the intercept.

	R²	0.723
	Adjusted R²	0.691
	R	0.850
	Std. Error	198.825
	n	30
	k	3
	Dep. Var.	TOT_SPEND
ANOVA table
Source	SS	df	MS	F	p-value
Regression	26,87,115.0495	3	8,95,705.0165	22.66	2.01E-07
Residual	10,27,811.1172	26	39,531.1968
Total	37,14,926.1667	29
Regression output					confidence interval
variables	coefficients	std. error	t (df=26)	p-value	95% lower	95% upper
Intercept	604.6127
PERSON*DAYS	13.7111	2.1053	6.513	6.65E-07	9.3835	18.0387
NATIONALITY	-147.0028	41.5606	-3.537	.0015	-232.4318	-61.5738
FIRST-TIME	-39.3412	92.1592	-0.427	.6730	-228.7772	150.0947

The regression model is:

TOT_SPEND = 604.6127 + 13.7111*PERSON*DAYS - 147.0028*NATIONALITY - 39.3412*FIRST-TIME

iii. Run the regression and state the estimated model for each Nationality distinguishing between first time and repeated visitors.

	R²	0.272
	Adjusted R²	0.218
	R	0.522
	Std. Error	316.489
	n	30
	k	2
	Dep. Var.	TOT_SPEND
ANOVA table
Source	SS	df	MS	F	p-value
Regression	10,10,466.8942	2	5,05,233.4471	5.04	.0138
Residual	27,04,459.2724	27	1,00,165.1582
Total	37,14,926.1667	29
Regression output					confidence interval
variables	coefficients	std. error	t (df=27)	p-value	95% lower	95% upper
Intercept	1,070.6006
NATIONALITY	-148.2985	66.1554	-2.242	.0334	-284.0381	-12.5589
FIRST-TIME	72.4729	144.1308	0.503	.6192	-223.2590	368.2048

The regression model is:

TOT_SPEND = 1,070.6006 - 148.2985*NATIONALITY + 72.4729*FIRST-TIME

iv. Which coefficients are statistically significant?

NATIONALITY

v. Run the model after you remove the non-significant coefficients. Compare with the model in (ii) and comment

	r²	0.265
	r	-0.515
	Std. Error	312.238
	n	30
	k	1
	Dep. Var.	TOT_SPEND
ANOVA table
Source	SS	df	MS	F	p-value
Regression	9,85,141.5833	1	9,85,141.5833	10.10	.0036
Residual	27,29,784.5834	28	97,492.3066
Total	37,14,926.1667	29
Regression output					confidence interval
variables	coefficients	std. error	t (df=28)	p-value	95% lower	95% upper
Intercept	1,161.3127
NATIONALITY	-167.8503	52.8029	-3.179	.0036	-276.0122	-59.6884