QUESTION 5
[19 MARKS]
The below data shows house prices and their respective features.
House p_r~~-
.. ·---- -- -1-- 2,60~000
2 _ .. }~89,500
bedroom toilets ERF~ize_sq?~imming pool
3
3.5
798
1
3
3.5
652
0
3 ?,97_8,525
4...
4.5
629
1
4 2,356,536
4
4.5
705
1
5 ~,456-,8_?~_
3
3
765
1
6 2,365,632
4
4.5
740
1
7 3,256,325
5
4.5
789
1
8 __id_56-.L545...,
4
4.5
806
1
--------·-·9 . 2,758,635
5
5.5
796
0,
10 ~,059~86
5
5.5
785
1
11
4
3.5
629
0
The data was run through regression at 95% confidence level, and below is the output.
SUMMARYOUTPUT
Regression Statistics
l\\/lultiple R
0.795299048
,~~_l_!~r~
~~jjusted Square
0.632500576
0.338501037
Standard Error
346416.6402
Observations
10
ANOVA
~egre,ssion
1 Residual
Total
In_te_rcep.!__
bedroom
toilets
ERFsiz~sguare m~ter
Swimming pool
df
55
MS
F
Significance F
4: l.03-E· +12 2.58E+ll 2.151366 i 0.21133526230
5 6E+ll, l.2E+ll
9 l.63E+l2
i
.,
l
Coefficients andard Em t Stat . P-value Lower 95% 'upper 95%ower 95.0'Jfpper 95.0%
302785.4823 · 1456554 0.207878 0.843526 -3441406.616 4046978 -3441407 4046978
393426.4856 375572.8 1.047537 0.342825· -57201'7,1817, . 1358867 -572014 1358867
-96722- .20708 365611 -0.26455 0.801915
12-88.4. 33712 1 1. 983.311 0.649638 0.544586
362822.513 285400.6 1.271275 0.259559,
-1036555.22, 843110.8. -1036555 843110.8
-3809.830648 I 6386.698 -3809.83 6386.698
-370822.9651 1096468 -370823 1096468
RESIDUALOUTPUT
Observation
Predicted price Residuals ,dard Residuals
li ?,535,530 64_470.17' 0.2496871
2 1,984,596 4904.006 0.018993
3 2,614,489 364036.2 1.40988
4 2,712,410 -355874 -1.37827
5 I 2,541,373 -84520.6 -0,32734
6 2,757,5.Q_~ -391873 -1.51769
7i 3,214,065 42260.31 0.16367
8' 2,842,542 ; 4i~cio~~-4•1.603398'
9 2,763~539 _-~904.01 -0.01899
10 3,112,189 -52502.7 -0.2033{
·' ·
PROBABILITYOUTPUT
Percentile
price
5' 1989500
15 I 2356536,
25 2365632
35 2456852
45 2600000
55• 2758635
65,I
-
2978525
7.5. \\i 3059686
85 3256325
95' 3256545'
Analyse the above data and multiple regression output and answer below.
5.1 Carefully study the regression output above and interpret the below results.
7