In 2014, a group of students was interested in investigatingprices of rental accommodation in suburbs of Brisbane that areclose to the CBD and collected information on a total of 200randomly chosen dwellings in four inner western suburbs. A subsetof this data, relating to rental apartments in these suburbs isincluded below. The variables are:

Per week: weekly rental price for the apartment($);

Bedrooms: number of bedrooms in theapartment;

Sqm: size of the apartment (m²)

Furnished: whether the apartment was furnishedor not (yes/no).

The values are;

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

Q1)

The students were interested in exploring the relationshipbetween apartment size and weekly rent. Using R, fit a linearregression relating weekly rent to apartment size; that is, a modelof the form:

per. week = ?0 + ?1 sqm + ?,

and answer the following questions:

(a) What is the MSE (mean-squared error) forthis regression? What are the degrees of freedom associated withthis value?

(b) Find a 95% confidence interval for theintercept parameter in this model. You may take relevant statisticsfrom the R output for your regression, but please show fullworking.

(c) Another group of students suggest thatapartment pricing is known to increase with apartment size at anaverage rate of $12 per square metre. Carry out a formal test ofthis hypothesis and interpret the resulting p-value, using ? =0.05.

(d) You intend to use your research to helpinform fair weekly rent for a friend, who is looking at renting anapartment of size 60 m2 . Using R, find a 95% prediction intervalfor the weekly rent of this apartment.

(e) Construct a residual and normal quantileplot for this analysis. Are there any issues with the underlyingassumptions of linearity and/or homoscedasticity?

Please answer this question by using R code !!!!!!! it is veryimportant