Question

An agent for a residential real estate company in a suburb located outside a major city has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward the​ 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 8​ one-bedroom apartments and the data are shown. Complete parts​ (a) through​ (e).

Monthly Rent ($)	Size (Square Feet)
925	850
1500	1200
850	950
1450	1150
1900	1800
900	750
1700	1250
1300	1050

a. Construct a scatter plot. Choose the correct graph below.

b. Use the​ least-squares method to determine the regression coefficients b₀ and b₁

b_{0 = __} b_{1 = __}  (Round to one decimal place as needed)

d. Predict the mean monthly rent for an apartment that has​ 1,000 square feet. (Round to the nearest cent as needed)

Answer 1

The Size (Square Feet) is the independent variable (X) while the Monthly Rent ($) is the dependent variable (Y)

a)

Graphically:

b)

The following data are passed:

Size	Rent
850	925
1200	1500
950	850
1150	1450
1800	1900
750	900
1250	1700
1050	1300

The independent variable is Size, and the dependent variable is Rent. In order to compute the regression coefficients, the following table needs to be used:

	Size	Rent	Size*Rent	Size2	Rent2
	850	925	786250	722500	855625
	1200	1500	1800000	1440000	2250000
	950	850	807500	902500	722500
	1150	1450	1667500	1322500	2102500
	1800	1900	3420000	3240000	3610000
	750	900	675000	562500	810000
	1250	1700	2125000	1562500	2890000
	1050	1300	1365000	1102500	1690000
Sum =	9000	10525	12646250	10855000	14930625

Based on the above table, the following is calculated:

Therefore, based on the above calculations, the regression coefficients (the slope b1, and the y-intercept b0) are obtained as follows:

Therefore, we find that the regression equation is:

Rent = 74.0796 + 1.1036 Size

i.e Rent = 74.1 + 1.1 Size

c)

When Size = 1000 then

Rent = 74.1 + 1.1 * 1000 = 1174.1

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