In 2014, a group of students was interested in investigating prices of rental ac
ID: 2923186 • Letter: I
Question
In 2014, a group of students was interested in investigating prices of rental accommodation in suburbs of Brisbane that are close to the CBD, and collected information on a total of 200 randomly chosen dwellings in four inner western surbubs.
A subset of this data, relating to rental apartments in these suburbs, is provided. The variables in this file are:
• per week: weekly rental price for the apart
available in the same folder as this assignment. The variables in this file are:
• per week: weekly rental price for the apartment ($);
• Bedrooms: number of bedrooms in the apartment;
• Furnished: whether the apartment was furnished or not (Yes/No).
Data:
Question 5 [4 marks] Finally, the group is interested to test whether rental prices for apartments vary with number of bedrooms. (For the purposes of this question, we will ignore the possible effect of whether the apartment is furnished.)
(a) Conduct an ANOVA analysis to assess what evidence there is that the average weekly rental price of apartments in these suburb varies between apartments with different numbers of bedrooms. You may use a computer to perform this test but please remember to interpret the p-value for this test in the context of the question. You should also show any relevant output from the computer to support your answer.
(b) It has been suggested that rental prices for 1-bedroom and 2-bedroom apartments are similar, but the 3-bedroom apartments are more expensive to rent. Assuming homoscedasticity (that is, that variances of weekly rental prices are similar across numbers of bedrooms), use the relevant sample statistics and the information from your ANOVA analysis in part (a) to calculate a 95% confidence interval for the
contrast 3-bed – (1-bed + 2-bed)/2. Interpret this interval.
Explanation / Answer
Answer:
Question 5 [4 marks] Finally, the group is interested to test whether rental prices for apartments vary with number of bedrooms. (For the purposes of this question, we will ignore the possible effect of whether the apartment is furnished.)
(a) Conduct an ANOVA analysis to assess what evidence there is that the average weekly rental price of apartments in these suburb varies between apartments with different numbers of bedrooms. You may use a computer to perform this test but please remember to interpret the p-value for this test in the context of the question. You should also show any relevant output from the computer to support your answer.
Analysis of Variance
Source
DF
Adj SS
Adj MS
F-Value
P-Value
bedroom
2
2023484
1011742
30.32
0.000
Error
100
3336728
33367
Total
102
5360212
Means
bedroom
N
Mean
StDev
95% CI
1
16
387.8
99.0
(297.2, 478.4)
2
63
431.3
106.6
(385.7, 477.0)
3
24
752.1
328.7
(678.1, 826.1)
Pooled StDev = 182.667
Model Summary
S
R-sq
R-sq(adj)
R-sq(pred)
182.667
37.75%
36.51%
32.83%
Calculated F=30.32, P=0.000 which is < 0.05 level.
There is enough evidence that average weekly rental price of apartments in these suburb varies between apartments with different numbers of bedrooms.
(b) It has been suggested that rental prices for 1-bedroom and 2-bedroom apartments are similar, but the 3-bedroom apartments are more expensive to rent. Assuming homoscedasticity (that is, that variances of weekly rental prices are similar across numbers of bedrooms), use the relevant sample statistics and the information from your ANOVA analysis in part (a) to calculate a 95% confidence interval for the
contrast 3-bed – (1-bed + 2-bed)/2. Interpret this interval.
3-bed – (1-bed + 2-bed)/2 = 752.1-(431.3+387.8)/2 =342.55
T value with 100 df at 95% level=1.984
S=182.667
Stand error of contrast = 182.667*sqrt( 1/24+1/(2*63)+1/(2*24))
=48.4796
95% CI = 342.55±1.984*48.4796
=(246.3665, 438.7335).
We are 95% confident that mean difference of all bedrooms with 3-bed – (1-bed + 2-bed)/2 falss in the interval (246.3665, 438.7335).
Source
DF
Adj SS
Adj MS
F-Value
P-Value
bedroom
2
2023484
1011742
30.32
0.000
Error
100
3336728
33367
Total
102
5360212
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