An agent for a property management company would like to be able to predict the monthly rental cost for apartments based on the size of the apartment as defined by square footage. A sample of the rent of 25 apartments in a college rental neighborhood was selected, and the information collected revealed the following:     Apartment Size (Sq. Ft.) Monthly Rent ($) 1 850 950 2 1,450 1,600 3 1,085 1,200 4 1,232 1,500 5 718 950 6 1,485 1,700 7 1,136 1,650 8 726 935 9 700 875 10 956 1,150 11 1,100 1,400 12 1,285 1,650 13 1,985 2,300 14 1,369 1,800 15 1,175 1,400 16 1,225 1,450 17 1,245 1,100 18 1,259 1,700 19 1,150 1,200 20 896 1,150 21 1,361 1,600 22 1,040 1,650 23 755 1,200 24 1,000 800 25 1,200 1,750

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An agent for a property management company would like to be able to predict the monthly rental cost for apartments based on the size of the apartment as defined by square footage. A sample of the rent of 25 apartments in a college rental neighborhood was selected, and the information collected revealed the following:

 

 

Apartment

Size (Sq. Ft.)

Monthly Rent ($)

1

850

950

2

1,450

1,600

3

1,085

1,200

4

1,232

1,500

5

718

950

6

1,485

1,700

7

1,136

1,650

8

726

935

9

700

875

10

956

1,150

11

1,100

1,400

12

1,285

1,650

13

1,985

2,300

14

1,369

1,800

15

1,175

1,400

16

1,225

1,450

17

1,245

1,100

18

1,259

1,700

19

1,150

1,200

20

896

1,150

21

1,361

1,600

22

1,040

1,650

23

755

1,200

24

1,000

800

25

1,200

1,750

e) Determine the coefficient of determination r2 and then completely interpret the meaning by using the language in the lecture notes. How useful do you think this regression model is for predicting the monthly rent? Explain.

f) Determine the residual for the 16th ordered pairs in the sample. Show all your   Note that x is the size column and y is the rent column in the data set….sketch a plot and show e16 on the plot.  Just follow the notes.

g) At the 0.05 level of significance, is there evidence of a significant linear relationship between the size of the apartment and the monthly rent? Always declare the meaning of B1 when we test or estimate the slope parameter.

h) Construct a 95% confidence interval estimate of the population slope B1. Do not forget to interpret the interval.  Always declare the meaning of B1 when we test or estimate the slope parameter…you will need to look up a tα/2, n-2.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Regr ssion Analysis: Rent versus Size
The regression equation is
Rent = 177 + 1.07 Size
Predictor
Coef SE Coef
Constant
Size
161.0 1.10 0.283
1.0651 0.1376 7.74 0.000
177.1
S = 194.595 R-Sq = 72.3% R-Sq (adj) = 71.1%
Analysis of Variance
Source
DF
SS
Regression
Residual Error 23 870949
Total
MS
1 2268777 2268777 59.91 0.000
37867
24 3139726
Predicted Values for New Observations
New
Obs
Fit
SE Fit
95% CI
(1153.0, 1331.5)
95% PI
1
1242.3
43.1
(829.9, 1654.6)
a)
State the regression model and completely interpret th
Transcribed Image Text:Regr ssion Analysis: Rent versus Size The regression equation is Rent = 177 + 1.07 Size Predictor Coef SE Coef Constant Size 161.0 1.10 0.283 1.0651 0.1376 7.74 0.000 177.1 S = 194.595 R-Sq = 72.3% R-Sq (adj) = 71.1% Analysis of Variance Source DF SS Regression Residual Error 23 870949 Total MS 1 2268777 2268777 59.91 0.000 37867 24 3139726 Predicted Values for New Observations New Obs Fit SE Fit 95% CI (1153.0, 1331.5) 95% PI 1 1242.3 43.1 (829.9, 1654.6) a) State the regression model and completely interpret th
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 SLR Assignment #18/19 

The monthly rent of college apartments 

An agent for a property management company would like to be able to predict the monthly rental cost for apartments based on the size of the apartment as defined by square footage. A sample of 25 apartments rent in a particular college rental neighborhood was selected, and the information collected revealed the following:

Apartment

Monthly Rent ($)

Size (Sq. Ft.)

1

950

850

2

1,600

1,450

3

1,200

1,085

4

1,500

1,232

5

950

718

6

1,700

1,485

7

1,650

1,136

8

935

726

9

875

700

10

1,150

956

11

1,400

1,100

12

1,650

1,285

13

2,300

1,985

14

1,800

1,369

15

1,400

1,175

16

1,450

1,225

17

1,100

1,245

18

1,700

1,259

19

1,200

1,150

20

1,150

896

21

1,600

1,361

22

1,650

1,040

23

1,200

755

24

800

1,000

25

1,750

1,200

 

A Minitab regression analysis was completed using the paired data from the above table.  First determine the dependant and independent variables, then use the Minitab output on the next page to complete the assignment. Note: Rent is Y and Size is X…

 

Regression Analysis: Rent versus Size 

 

The regression equation is

Rent = 177 + 1.07 Size



Predictor    Coef  SE Coef     T      P

Constant    177.1    161.0  1.10  0.283

Size       1.0651   0.1376  7.74  0.000



S = 194.595   R-Sq = 72.3%   R-Sq(adj) = 71.1%



Analysis of Variance

Source          DF       SS       MS      F      P

Regression       1  2268777  2268777  59.91  0.000

Residual Error  23   870949    37867

Total           24  3139726



Predicted Values for New Observations

New

Obs     Fit    SE Fit       95% CI            95% PI

  1   1242.3    43.1 (1153.0, 1331.5) (829.9, 1654.6)

 

  1. a) State the regression model and completely interpret the meaning of b0 and b1.

 

  1. b) Predict the monthly rent and the standard error { SE(ŷ1100) } for an apartment that has 1,100 square feet. 

 

  1. c) Why would it not be appropriate to use the model to predict the monthly rent for apartments that have 500 square feet?

 

  1. d) Your friends Jim and Jenn are considering signing a lease for an apartment in the college rental neighborhood that the sample was taken from; . They are trying to decide between two apartments, one with 1,000 square feet for a monthly rent of $1,275 and the other with 1,200 square feet for a monthly rent of $1,425. What would you recommend to them?  Explain by estimating y for two different sized apartments and then comparing the rent for each

 

  1. e) Determine the coefficient of determination r2 and then completely interpret the meaning. How useful do you think this regression model is for predicting the monthly rent? Explain.  What percentage of the variability in the estimate of Y is accounted for by variables that are not identified and not used in this model?

 

  1. g) At the 0.05 level of significance, is there evidence of a significant linear relationship between the size of the apartment and the monthly rent?  State the meaning of B1 first.  This is a t test for B1.

 

  1. h) Construct a 95% confidence interval estimate of the population slope B1.  Don’t forget to interpret the interval.  Always declare the meaning of B1 when we test or estimate the slope parameter…use b1 ± t α/2,n-2 (Sb1).

 

  1. i) Determine a 95% interval estimate for the average rent of apartments with 1000 square feet.  Determine ŷ1000 and interpret the interval estimate for the average rent completely.

 

  1. j) Predict the rent of an apartment with 1650 square feet.  What is the S.D. of this estimate?  ie: determine ŷ1650 and SE(ŷ1650)…



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