Question

An airport shuttle service wants to determine the length of time it would take to transport passengers from various locations to a major metropolitan airport during nonpeak hours. A sample of 16 trips on a particular day during nonpeak hours indicates the following:

Distance (miles)	Time (minutes)	Distance (miles)	Time (minutes)
35.0	29	15.7	41
19.5	35	18.4	27
25.4	70	20.2	37
27.0	55	21.8	36
10.3	19	24.3	40
11.6	18	30.3	21
16.1	23	9.2	20
14.3	40	12.1	24

1. Using Excel, create a scatter diagram for distance and time. This what should be your Y (dependent) variable and what should be your X (independent) variable. No need to submit the results.

2. Calculate the covariance between distance and time using Excel. What is its value?

3. Calculate the correlation coefficient. What is its value?

4. Calculate the least-squares regression equation using distance as an independent variable and time as a dependent variable______ Intercept:_____

5. Is the intercept coefficient significant at the 5% level? Yes or No?

6. Is the slope coefficient significant at the 5% level? Yes or No?

Answer 1

a) A scatter diagram for distance and time.

Distance(X)	Time(Y)	(y-ybar)^2	(x-xbar)^2	(x-xbar)(y-ybar)
35	29	19.7136	241.8025	-69.042
19.5	35	2.4336	0.0025	0.078
25.4	70	1336.6336	35.4025	217.532
27	55	464.8336	57.0025	162.778
10.3	19	208.5136	83.7225	132.126
11.6	18	238.3936	61.6225	121.204
16.1	23	108.9936	11.2225	34.974
14.3	40	43.0336	26.5225	-33.784
15.7	41	57.1536	14.0625	-28.35
18.4	27	41.4736	1.1025	6.762
20.2	37	12.6736	0.5625	2.67
21.8	36	6.5536	5.5225	6.016
24.3	40	43.0336	23.5225	31.816
30.3	21	154.7536	117.7225	-134.974
9.2	20	180.6336	105.0625	137.76
12.1	24	89.1136	54.0225	69.384
311.2	535	3007.9376	838.88	656.95
19.45	33.44

b) The covariance between distance and time is given by,

= 656.95 / 16 [ from the table above]

= 41.059

c)  The correlation coefficient is given by,

  

= 0.413

d) the least-squares regression equation using distance as an independent variable and time as a dependent variable

b = 656.95 / 838.88 = 0.783, Slope

a = 33.44 - 0.783*19.45 = 18.211, Intercept

y = 18.211 + 0.783 x

Distancex	Timey	yhat	(y-yhat)^2
35	29	45.616	276.0915
19.5	35	33.4795	2.31192
25.4	70	38.0992	1017.661
27	55	39.352	244.8599
10.3	19	26.2759	52.93872
11.6	18	27.2938	86.37472
16.1	23	30.8173	61.11018
14.3	40	29.4079	112.1926
15.7	41	30.5041	110.1639
18.4	27	32.6182	31.56417
20.2	37	34.0276	8.835162
21.8	36	35.2804	0.517824
24.3	40	37.2379	7.629196
30.3	21	41.9359	438.3119
9.2	20	25.4146	29.31789
12.1	24	27.6853	13.58144
311.2	535	535.0456	2493.462

SSE = 2493.462

e) test statistic of intercept is given by,

  

t = 0.51

p-vaue = 0.6175 > 0.05

No, at level 0.05, intercept coefficient is not significant.

f) test statistic of slope coefficient is given by,

  

t = 1.70

p-value = 0.1098 < 0.05

No, at level 0.05, slope coefficient is not significant.

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