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 ($) 1 850 950 2 1,450 1,600 3 1,085 1,200 4 1,232 1,500 5 718 950 6 1,485 1,700 7 1,136 1,650 8 726 935 9 700 875 10 956 1,150 11 1,100 1,400 12 1,285 1,650 13 1,985 2,300 14 1,369 1,800 15 1,175 1,400 16 1,225 1,450 17 1,245 1,100 18 1,259 1,700 19 1,150 1,200 20 896 1,150 21 1,361 1,600 22 1,040 1,650 23 755 1,200 24 1,000 800 25 1,200 1,750
An agent for a property management company would like to be able to predict the monthly rental cost for apartments based on the size of the apartment as defined by square footage. A sample of the rent of 25 apartments in a college rental neighborhood was selected, and the information collected revealed the following:
|
Apartment |
Size (Sq. Ft.) |
Monthly Rent ($) |
|
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
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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: 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)
- a) State the regression model and completely interpret the meaning of b0 and b1.
- b) Predict the monthly rent and the standard error { SE(ŷ1100) } for an apartment that has 1,100 square feet.
- c) Why would it not be appropriate to use the model to predict the monthly rent for apartments that have 500 square feet?
- 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
- 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?
- 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.
- 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).
- 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.
- 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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