Question

An agent for a residential real estate company in a large city has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward that goal, the agent would like to use the size of an apartment, as defined by square footage to predict the monthly rental cost. The agent selects a sample of 25 apartments in a particular residential neighborhood and collects the following data:

Size (square feet)	Rent ($)
850	1950
1450	2600
1085	2200
1232	2500
718	1950
1485	2700
1136	2650
726	1935
700	1875
956	2150
1100	2400
1285	2650
1985	3300
1369	2800
1175	2400
1225	2450
1245	2100
1259	2700
1150	2200
896	2150
1361	2600
1040	2650
755	2200
1000	1800
1200	2750

(a) Determine the coefficient of determination, r², and interpret its meaning.

(b) Determine the standard error of the estimate (Syx).

(c) How useful do you think this regression model is for predicting the monthly rent?

(d) Can you think of other variables that might explain the variation in monthly rent?

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
850	1950	81407.50	190444.96	124513.65
1450	2600	99023.50	45624.96	67215.65
1085	2200	2532.10	34744.96	9379.65
1232	2500	9347.02	12904.96	10982.85
718	1950	174155.98	190444.96	182118.45
1485	2700	122276.10	98344.96	109659.65
1136	2650	0.46	69484.96	179.25
726	1935	167542.86	203761.96	184767.05
700	1875	189503.50	261529.96	222622.65
956	2150	32155.66	55884.96	42391.25
1100	2400	1247.50	184.96	-480.35
1285	2650	22404.10	69484.96	39455.65
1985	3300	721956.10	834664.96	776267.65
1369	2800	54606.34	171064.96	96650.05
1175	2400	1574.50	184.96	539.65
1225	2450	8042.50	4044.96	5703.65
1245	2100	12029.70	82024.96	-31412.35
1259	2700	15296.74	98344.96	38786.05
1150	2200	215.50	34744.96	-2736.35
896	2150	57274.06	55884.96	56575.25
1361	2600	50931.46	45624.96	48205.25
1040	2650	9085.90	69484.96	-25126.35
755	2200	144643.30	34744.96	70891.65
1000	1800	18311.502	343864.960	79351.648
1200	2750	4183.502	132204.960	23517.648

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	28383	59660	1999747.44	3139726.0	2130018.80
mean	1135.32	2386.40	SSxx	SSyy	SSxy

R² =    (Sxy)²/(Sx.Sy) =   0.7226 =  72%

.............

SSE=   (SSxx * SSyy - SS²xy)/SSxx =    870949.455
      
std error ,Syx =    √(SSE/(n-2)) =    194.595

S_yx measures the typical difference between an​ apartment's actual rent and the rent predicted by the regression equation.
................

R2= 72%

so, this regression model is very useful for predicting the monthly rate and std error is also small

............

other variables can be:

parking facility

location of apartment

furniture in apartment

thanks

upvote please