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 suburbs. 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 apartment ($);

• Bedrooms: number of bedrooms in the apartment;

• Sqm: size of the apartment (m2)

• Furnished: whether the apartment was furnished or not (Yes/No).

Data: Per week, Bedrooms, Sqm, Furnished

265,2,59,No

305,2,70,No

300,1,72,No

320,3,66,No

340,2,113,Yes

330,2,58,Yes

355,2,63,No

345,2,57,Yes

355,2,61,No

360,2,114,Yes

355,2,75,Yes

360,2,68,No

365,2,64,No

370,1,69,No

390,2,73,Yes

380,2,85,Yes

390,2,56,Yes

370,2,56,Yes

385,2,59,Yes

380,2,65,Yes

385,2,62,Yes

400,2,65,No

415,2,69,Yes

400,3,63,No

405,3,70,No

420,2,77,No

435,2,84,Yes

435,2,83,Yes

455,2,73,Yes

450,2,72,Yes

485,2,68,No

500,2,76,Yes

535,2,97,No

290,1,60,No

305,1,63,Yes

330,2,65,No

310,2,70,No

335,2,64,No

330,2,62,No

345,2,79,No

355,1,81,No

340,2,66,No

345,1,60,No

345,2,64,No

355,2,73,No

385,2,61,No

380,2,78,No

405,2,81,No

410,2,76,Yes

430,2,80,No

440,2,61,No

450,3,86,No

485,3,91,No

500,1,87,No

545,1,97,Yes

345,3,86,No

400,2,72,No

400,2,74,No

480,2,73,Yes

755,3,87,No

760,3,77,No

770,3,113,No

824,2,109,No

860,3,104,No

295,1,70,No

290,1,54,No

295,1,61,No

325,1,61,No

340,2,56,No

355,2,61,No

365,2,95,No

420,1,75,No

420,2,66,No

440,2,74,No

480,3,72,No

465,3,87,No

470,1,87,Yes

490,1,81,Yes

495,2,76,No

505,2,97,No

530,2,77,No

545,2,97,No

560,2,79,No

550,2,78,No

560,3,75,No

565,1,96,Yes

580,2,85,Yes

605,3,84,No

605,2,93,Yes

610,2,78,Yes

620,2,87,No

665,2,88,No

700,2,80,No

750,3,97,Yes

740,3,124,No

805,3,101,No

860,3,98,No

960,3,123,Yes

990,3,102,Yes

1195,3,133,No

1190,3,137,No

1405,3,148,Yes

1490,3,154,No

Question 4)

Finally, the students were interested in exploring the relationship between apartment size and weekly rent. Using R, fit a linear regression relating weekly rent to apartment size; that is, a model of the form:

Per week = β0 + β1 sqm + ε, and answer the following questions:

(a) Find a 95% confidence interval for the intercept parameter in this model. You may take relevant statistics from the R output for your regression, but please show full working.

(b) Another group of students suggest that apartment pricing is known to increase with apartment size at an average rate of $12 per square meter. Carry out a formal test of this hypothesis and interpret the resulting p-value, using α = 0.05.

Answer 1

Running a simple linear regression in R,

Substituting the estimated coefficients in the model equation, we get,

Per week = -268.3769 + 9.5674 sqm

(a)  95% confidence interval for the intercept parameter is given by (-369.941568,-166.81225)

(b)

Since the slope coefficient for the predictor is nothing but the average increase in the apartment pricing for a unit increase in square meter.Hence we have to test

Vs

Running a t test for slope in R,

Since the p value of the test 0.0001 < 0.05, there is not enough evidence to support the null hypothesis.Hence H₀ is rejected at 5% level.

We may conclude that the claim of the sudents that apartment pricing is known to increase with apartment size at an average rate of $12 per square meter is not true.