Question

A suburban hotel derives its revenue from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied.

Day		Revenue			Occupied		Day		Revenue			Occupied
1		$	1,452		60		14		$	1,425		31
2			1,361		20		15			1,445		51
3			1,426		21		16			1,439		62
4			1,470		80		17			1,348		45
5			1,456		70		18			1,450		41
6			1,430		29		19			1,431		62
7			1,354		30		20			1,446		47
8			1,442		21		21			1,485		43
9			1,394		15		22			1,405		38
10			1,459		36		23			1,461		36
11			1,399		41		24			1,490		30
12			1,458		35		25			1,426		65
13			1,537		51

Answer 1

the scatterplot of the given data is

using excel>data>data analysis>Regression

we have

Regression Analysis
Regression Statistics
Multiple R	0.333809151
R Square	0.11142855
Adjusted R Square	0.072795008
Standard Error	41.20806786
Observations	25
ANOVA
	df	SS	MS	F	Significance F
Regression	1	4897.748295	4897.748295	2.884243735	0.102940121
Residual	23	39056.4117	1698.104857
Total	24	43954.16
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1399.801394	22.61097777	61.90804345	4.33867E-27	1353.027023	1446.575765
Occupied	0.843363346	0.496590884	1.698306137	0.102940121	-0.183913166	1.870639857

the p value of F stat is 0.1029 which is greater than 0.05 so we conclude that there exist no relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant.

Using t test

the value of r = 0.334

n = 25

the null and alternative hypothesis is

H0: ρ ≤ 0;

H1: ρ > 0 (one tailed)

=

= 1.70

1. the decision rule for 0.01 significance level: is reject Ho if t > 2.50

since value of test stat t is < 2.50 so reejct Ho

2.] 11.1 percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied