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? (f). Monthly Rent? ($) 925 1 comma 450 825 1 comma 450 1 comma 950 975 1 comma 800 1 comma 300 Size? (Square Feet) 850 1 comma 200 950 1 comma 150 2 comma 000 650 1 comma 250 1 comma 050 a. Construct a scatter plot. Choose the correct graph below. A. 0 2,000 0 2,000 Size (Sq ft) Rent ($) A scatter plot has a horizontal axis labeled Size (in square feet) from 0 to 2000 in increments of 400 and a vertical axis labeled Rent ($) from 0 to 2000 in increments of 400. A series of plotted points fall exactly on a line that falls from left to right, where the points range from (650,1500) to (2,000,500). All coordinates are approximate. B. 0 2,000 0 2,000 Size (Sq ft) Rent ($) A scatter plot has a horizontal axis labeled Size (in square feet) from 0 to 2000 in increments of 400 and a vertical axis labeled Rent ($) from 0 to 2000 in increments of 400. A series of plotted points fall exactly on a line that rises from left to right, where the points range from (650,650) to (2,000,2000). All coordinates are approximate. C. 0 2,000 0 2,000 Size (sq ft) Rent ($) A scatter plot has a horizontal axis labeled Size (in square feet) from 0 to 2000 in increments of 400 and a vertical axis labeled Rent ($) from 0 to 2000 in increments of 400. A series of plotted points are clustered around a line that falls from left to right passing through the points (800,1200) and (1200,1000). All coordinates are approximate. D. 0 2,000 0 2,000 Size (Sq ft) Rent ($) A scatter plot has a horizontal axis labeled Size (in square feet) from 0 to 2000 in increments of 400 and a vertical axis labeled Rent ($) from 0 to 2000 in increments of 400. A series of plotted points are clustered around a line that rises from left to right passing through the points (1200,1400) and (1600,1700). All coordinates are approximate. b. Use the? least-squares method to determine the regression coefficients b 0 and b 1. b 0 equals 25.3 ?(Round to one decimal place as? needed.) b 1 equals 0.8 ?(Round to one decimal place as? needed.) c. Interpret the meaning of b 0 and b 1 in this problem. Choose the correct answer below. A. For each increase of 1 square foot in? space, the monthly rent is expected to increase by b 1 do l l ars. Since X cannot be? zero, b 0 has no practical interpretation. B. For each increase of 1 square foot in? space, the monthly rent is expected to increase by b 0 do l l ars. Since X cannot be? zero, b 1 has no practical interpretation. C. For each increase of 1 square foot in? space, the monthly rent is expected to increase by b 0 do l l ars. Apartments in this neighborhood cost at least b 1 do l l ars. D. For each increase of 1 square foot in? space, the monthly rent is expected to increase by b 1 do l l ars. Apartments in this neighborhood cost at least b 0 do l l ars. d. Predict the mean monthly rent for an apartment that has? 1,000 square feet. The predicted mean monthly rent for such an apartment is ?$ 25 25. ?(Round to the nearest cent as? needed.) e. Why would it not be appropriate to use the model to predict the monthly rent for apartments that have 500 square? feet? A. The model predicts that the monthly rent for an apartment that has 500 square feet would be unrealistically low. B. The size of an apartment has no effect on the monthly? rent, according to this model. There must be another factor that contributes to the rent price. C. The correlation between an? apartment's size and its monthly rent is too weak to use this model for such a prediction. D. An apartment with 500 square feet is outside the relevant range for the independent variable. f. Two people are considering signing a lease for an apartment in this neighborhood. 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. Based on? (a) through? (d), which apartment is a better? deal? Based on? (a) through? (d), the apartment with 1,000 1,200 1,000 square feet is the better deal. Click to select your answer(s).

Answer 1

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.

The dataset is of 8 observations.

monthly rent	size
900	750
1500	1250
850	1050
1550	1250
1950	1800
950	700
1800	1350
1250	1050

a) We have to draw scatter plot of the data.

We can draw scatter plot in excel.

Stepe :

ENTER data into excel sheet --> select data range --> Insert --> Scatter --> Select first option --> ok

From the scatter plot we can say that there is positive relationship between two variables.

b. Use the? least-squares method to determine the regression coefficients b 0 and b 1.

b0 = 142.61

b1 = 0.75

The regression equation is,

monthly rent = 100.69 + 1.08*size

Interpretation of intercept and slope :

If we fix size as 0 then monthly rent will be 100.69 unit.

For one unit change in size will be 1.08 unit increase in monthly rent.

d. Predict the mean monthly rent for an apartment that has? 1,000 square feet

Now we have to find monthly rent for size = 1000

This we can find by using regression equation.

monthly rent = 100.69 + 1.08*size

monthly rent = 100.69 + 1.08*1000 = 1181.61