Question

Data for a sample of 30 apartments in a particular neighborhood are provided in the worksheet. You want to see if there is a direct relationship between Size of the Apartment and Rent.

Rent	Size
950	850
1500	1450
1150	1085
1400	1232
950	718
1700	1485
1550	1136
935	726
875	700
1050	956
1400	1100
1650	1500
1875	1985
1800	1674
1395	1223
1375	1225
1100	1300
1500	1345
1200	1150
1150	896
1100	1361
1150	1040
1200	755
800	1000
850	1200
500	650
900	1100
1000	900
1025	1000
900	953

Approximately what percentage of the variation in Rent is explained by the regression model you derived?

Place your answer, rounded to 1 decimal place.

Answer 1

We need to find the coefficient of determination r², which is the square of the correlation coefficient r.

To calculate pearsons co efficient r

From the Given data, the following is calculated (Tables given at the end)

SUM (x) = 35930, SUM (y) = 33695, SUM (xy) = 42732795,

SUM (x²) = 46125250, (SUM x)² = (35930)²= 1290964900

SUM (y²) = 40580157, (SUM y)² = (33695)² = 1135353025

SUM (x) * SUM (y) = 35930 x 33695 = 1210661350

n = 30

Substituting these in the equation for r, we get

Therefore r2 = 0.817384 * 0.817384 = 0.668 or 66.8%

Therefore, approximately 66.8% of the variation in Rent is explained by the regression model.

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Count	x	y	xy	x2	y2
1	950	850	807500	902500	722500
2	1500	1450	2175000	2250000	2102500
3	1150	1085	1247750	1322500	1177225
4	1400	1232	1724800	1960000	1517824
5	950	718	682100	902500	515524
6	1700	1485	2524500	2890000	2205225
7	1550	1136	1760800	2402500	1290496
8	935	726	678810	874225	527076
9	875	700	612500	765625	490000
10	1050	956	1003800	1102500	913936
11	1400	1100	1540000	1960000	1210000
12	1650	1500	2475000	2722500	2250000
13	1875	1985	3721875	3515625	3940225
14	1800	1674	3013200	3240000	2802276
15	1395	1223	1706085	1946025	1495729
16	1375	1225	1684375	1890625	1500625
17	1100	1300	1430000	1210000	1690000
18	1500	1345	2017500	2250000	1809025
19	1200	1150	1380000	1440000	1322500
20	1150	896	1030400	1322500	802816
21	1100	1361	1497100	1210000	1852321
22	1150	1040	1196000	1322500	1081600
23	1200	755	906000	1440000	570025
24	800	1000	800000	640000	1000000
25	850	1200	1020000	722500	1440000
26	500	650	325000	250000	422500
27	900	1100	990000	810000	1210000
28	1000	900	900000	1000000	810000
29	1025	1000	1025000	1050625	1000000
30	900	953	857700	810000	908209
Total	35930.00	33695.00	42732795.00	46125250.00	40580157.00

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