Question

In: Statistics and Probability

This sample data was collected to study the relationship between the rent charged with the size...

This sample data was collected to study the relationship between the rent charged with the size of a dwelling. Identify the dependent variable and independent variable. Do they have a cause and effect relationship? Explain. Run Regression on this data. Make sure to check the boxes for charts, normal distribution, residual charts, etc. Write the null and alternate hypotheses to test if the linear relationship (slope) is significant or not. Conduct F test to determine if you are going to accept or reject the nul hypothesis. You can use p-value test also. Write down the regression model (Linear equation) that the regression program output.

square feet/ Rent

655   1975
663   1581
718   1429
665   1350
715   1633
903   1807
708   1632
785   1528
955   1800
525   1206
630   1421
731   1870
694   1858
685   1782
675   1750
750   1440
610   1212
531   1176
750   1270
675   1503
725   1595
820   1795
660   998
535   1080
628   1337
434   1075
775   1574
707   1556
702   1300
872   1400
578   1200
470   1450
770   1590
784   1525
872   1575
675   1478
768   1450
797   1750
600   1150
660   1850
925   1650
650   1275
550   1100
665   1398
916   1600
850   1350
750   1550
900   1300
690   1600
574   1300
800   1500
775   1400
873   1650
814   1575
739   1600
820   1425
665   1270

Expert Solution

Using Excel, go to Data, select Data Analysis, choose Regression. Put square feet in X input range and rent in Y input range. Tick Residual Plot, Normal Probability Plot and Line Fit Plot.

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.500
R Square	0.250
Adjusted R Square	0.236
Standard Error	198.486
Observations	57

ANOVA
	df	SS	MS	F	Significance F
Regression	1	722265.743	722265.743	18.333	0.000
Residual	55	2166819.239	39396.713
Total	56	2889084.982

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	781.877	165.695	4.719	0.000	449.816	1113.937
Square Feet	0.978	0.228	4.282	0.000	0.520	1.436

RESIDUAL OUTPUT

Observation	Predicted Y	Residuals
1	1422.689	552.311
2	1430.516	150.484
3	1484.325	-55.325
4	1432.473	-82.473
5	1481.390	151.610
6	1665.318	141.682
7	1474.541	157.459
8	1549.874	-21.874
9	1716.191	83.809
10	1295.505	-89.505
11	1398.231	22.769
12	1497.043	372.957
13	1460.845	397.155
14	1452.039	329.961
15	1442.256	307.744
16	1515.632	-75.632
17	1378.664	-166.664
18	1301.375	-125.375
19	1515.632	-245.632
20	1442.256	60.744
21	1491.173	103.827
22	1584.115	210.885
23	1427.581	-429.581
24	1305.288	-225.288
25	1396.274	-59.274
26	1206.476	-131.476
27	1540.090	33.910
28	1473.563	82.437
29	1468.671	-168.671
30	1634.989	-234.989
31	1347.357	-147.357
32	1241.696	208.304
33	1535.198	54.802
34	1548.895	-23.895
35	1634.989	-59.989
36	1442.256	35.744
37	1533.242	-83.242
38	1561.614	188.386
39	1368.881	-218.881
40	1427.581	422.419
41	1686.841	-36.841
42	1417.798	-142.798
43	1319.964	-219.964
44	1432.473	-34.473
45	1678.036	-78.036
46	1613.466	-263.466
47	1515.632	34.368
48	1662.383	-362.383
49	1456.931	143.069
50	1343.444	-43.444
51	1564.549	-64.549
52	1540.090	-140.090
53	1635.967	14.033
54	1578.245	-3.245
55	1504.870	95.130
56	1584.115	-159.115
57	1432.473	-162.473

Percentile	Y
0.877	998
2.632	1075
4.386	1080
6.140	1100
7.895	1150
9.649	1176
11.404	1200
13.158	1206
14.912	1212
16.667	1270
18.421	1270
20.175	1275
21.930	1300
23.684	1300
25.439	1300
27.193	1337
28.947	1350
30.702	1350
32.456	1398
34.211	1400
35.965	1400
37.719	1421
39.474	1425
41.228	1429
42.982	1440
44.737	1450
46.491	1450
48.246	1478
50.000	1500
51.754	1503
53.509	1525
55.263	1528
57.018	1550
58.772	1556
60.526	1574
62.281	1575
64.035	1575
65.789	1581
67.544	1590
69.298	1595
71.053	1600
72.807	1600
74.561	1600
76.316	1632
78.070	1633
79.825	1650
81.579	1650
83.333	1750
85.088	1750
86.842	1782
88.596	1795
90.351	1800
92.105	1807
93.860	1850
95.614	1858
97.368	1870
99.123	1975

1. Dependent variable - Rent

Independent variable - Square feet

2. Do they have a cause and effect relationship? Explain.

H0: There exists no cause and effect relationship between square feet and rent

H1: There exists a cause and effect relationship between square feet and rent

p-value (Sqaure feet) = 0.000

Since p-value is less than 0.05, we reject the null hypothesis.

So, there exists a a cause and effect relationship between square feet and rent.

3. H0: There exists no linear relationship between square feet and rent

H1: There exists a linear relationship between square feet and rent

p-value (Significance F) = 0.000

Since p-value is less than 0.05, we reject the null hypothesis.

So, there exists a linear relationship between square feet and rent.

4. Regression model

Rent = 781.877 + 0.978*Sqaure Feet

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