Question

Question 2 (Using PHStat)

A young researcher wants to know what factors affect the Number of weekly riders. You are asked to help the young researcher to make statistical analysis.

1. Develop two (2) hypotheses
2. Using simple linear regression analysis with a significance level of 5% as the basis of your analysis, please conduct the analysis and interpret the results for both of the hypotheses that you developed.

City	Number of weekly riders	Price per week	Population of city	Monthly income of riders	Average parking rates per month
1	192,000	$15	1,800,000	$5,800	$50
2	190,400	$15	1,790,000	$6,200	$50
3	191,200	$15	1,780,000	$6,400	$60
4	177,600	$25	1,778,000	$6,500	$60
5	176,800	$25	1,750,000	$6,550	$60
6	178,400	$25	1,740,000	$6,580	$70
7	180,800	$25	1,725,000	$8,200	$75
8	175,200	$30	1,725,000	$8,600	$75
9	174,400	$30	1,720,000	$8,800	$75
10	173,920	$30	1,705,000	$9,200	$80
11	172,800	$30	1,710,000	$9,630	$80
12	163,200	$40	1,700,000	$10,570	$80
13	161,600	$40	1,695,000	$11,330	$85
14	161,600	$40	1,695,000	$11,600	$100
15	160,800	$40	1,690,000	$11,800	$105
16	159,200	$40	1,630,000	$11,830	$105
17	148,800	$65	1,640,000	$12,650	$105
18	115,696	$102	1,635,000	$13,000	$110
19	147,200	$75	1,630,000	$13,224	$125
20	150,400	$75	1,620,000	$13,766	$130
21	152,000	$75	1,615,000	$14,010	$150
22	136,000	$80	1,605,000	$14,468	$155
23	126,240	$86	1,590,000	$15,000	$165
24	123,888	$98	1,595,000	$15,200	$175
25	126,080	$87	1,590,000	$15,600	$175
26	151,680	$77	1,600,000	$16,000	$190
27	152,800	$63	1,610,000	$16,200	$200

Answer 1

a)

I want to test if there is any significant linear relationship between the number of Weekly Riders and the price per week.

The null hypothesis, there is no significant linear relationship between the number of Weekly Riders and the price per week. This is tested against an alternative hypothesis, there is a significant linear relationship between the number of Weekly Riders and the price per week.

I also wish to test if there is any significant linear relationship between the number of Weekly Riders and the average parking rates per month.

The null hypothesis, there is no significant linear relationship between the number of Weekly Riders and the population of the city. This is tested against an alternative hypothesis, there is a significant linear relationship between the number of Weekly Riders and Population of the city.

b)

(i)

Simple Linear Regression Analysis
Regression Statistics
Multiple R	0.9660
R Square	0.9331
Adjusted R Square	0.9304
Standard Error	5620.1139
Observations	27

ANOVA
	df	SS	MS	F	Significance F
Regression	1	11007513388.7432	11007513388.7432	348.4970	0.0000
Residual	25	789642015.1086	31585680.6043
Total	26	11797155403.8519

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95%	Upper 95%
Intercept	197208.3412	2266.4811	87.0108	0.0000	192540.4361	201876.2463	192540.4361	201876.24633
Price per week	-744.7487	39.8942	-18.6681	0.0000	-826.9124	-662.5849	-826.9124	-662.58494

With F(1, 26) = 348.49, P<5%, I REJECT ho at 5% level of significance and conclude that there is a significant linear relationship between the number of Weekly Riders and the price per week.

regression equation: Numberofweeklyriders = 197208.3412 - 744.7487*price per week

(ii)

Simple Linear Regression Analysis
Regression Statistics
Multiple R	0.8976
R Square	0.8056
Adjusted R Square	0.7978
Standard Error	9577.2438
Observations	27

ANOVA
	df	SS	MS	F	Significance F
Regression	1	9504065441.3508	9504065441.3508	103.6164	0.0000
Residual	25	2293089962.5010	91723598.5000
Total	26	11797155403.8519

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95%	Upper 95%
Intercept	-313732.0555	46578.2102	-6.7356	0.0000	-409661.6752	-217802.4359	-409661.6752	###########
Populationofcity	0.2820	0.0277	10.1792	0.0000	0.2249	0.3390	0.2249	0.33903

With (F(1, 16) = 103.6, P<5%, I REJECT ho and conclude that there is a significant linear relationship between the number of Weekly Riders and Population of the city.

regression equation: Numberofweeklyriders = -313732 + 0.2820*population