Question

ne goal, the agent 00 1,250 1,050 1,250 1,300 700 1350 1,100 aConstruct a scaer piot. Chosse the comect graph below O A ов. o c. b. Use the leasi-squares method to determine the regression coefficients bo and b Round to one decimal place as Round to one decimal place as c. Interpret the meaning of bo and by in this probilem Choose the correct answer bellow O A. For each increase of 1 square foot in space, the monthly rent is expected to increase by OB. Foreach ioease of 1 saare tot in space, he morney rent is expected toincrease by O C. For each increase of 1 square fook in space, the montly rent is expected to increase by O D. For each increase of 1 square foot in space, the monely rent is expected to increaso by bp dollars. Apartments in this neighborhood cost at least b, dollars bt daillars. Since X cannot be zero, Dp has no practical interpretation by dollars. Apartments in this neighborhood cost at least bo doillans bo dolars. Since X cannot be zer, by has no pracical inberpretation d.Predict ยาก mean monthy rent for an apartment that has 1,000 square feet. The predicted mean monthly rent for such an apartment is 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? OA. The size of an apartrent has no effect on the montly rent, according to tis model. There O B. An apartment with 500 square feet is outside the relevant range for the Independent variabls OC. The corelaton between an spartment's size and itsrn to weak to use tis modt O D. The model predicts that the monthly rent for an apartment that has 500 square feet would be must be another factor that contributes to the rent price. for such a prediction 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 monihly rent of $1.425. Based on (a) through (d), which apartment is a better deal? Based on (a) through (d), the apartment with (1) square feet is the better deal. (1) O 1,200 O 1,000

Answer 1

a) We can use excel to draw scatter plot , Select the both data sets ( excluding headings and go to Insert menu -->Charts --> select Scatter plot )

Because we are predicting the monthly rent (Y) based on size (X), first make column(A) for size and then column(B) for rent.

Answer : option D)

b) Lease square regression equation.

Y = b₀ + b₁ *x

Or Monthly rent = b₀ + b₁ * Size

b₀ is Intercept , we can find intercept using excel function =INTERCEPT( Y data set column range, x data set column range)

b₁ is Slope , we can find intercept using excel function =SLOPE( Y data set column range, x data set column range )

Therefore , b₀ = 120.7 and b₁ = 1.0

Equation of regression line is ,

Monthly rent = 120.7 + 1.0* Size

c)

Interpretation of slope b₁ = 1.0 and b₀ = 120.7

Option c) For each increase of 1 square foot in space, the monthly rent is expected to increase by b₁ dollars.

Apartments in the neighborhood cost at least b₀ dollars.

d) We are given Size (X) = 1000 , and we are asked to predict Monthly rent (y)

Monthly rent = 120.7 + 1.0* 1000 = 120.7 + 1000

Monthly rent = 1121

e) Option B) An apartment with 500 square feet is outside the relevant range for the independent variable ( Size )

f) We are given Monthly rent =1275 for size =1000 ,

Using regression equation For size = 1000 Monthly rent = 1121

Therefore residual = Y – = 1275 – 1121 = 154

For size = 1200 , we are given Monthly rent =1425

Using regression equation For size = 1000,

Monthly rent = 120.7+(1.0*1200) = 1321

Therefore residual = Y – = 1425 – 1321 = 104

So apartment with size = 1200 and Monthly rent = 1425 has less residual

Therefore the apartment with size 1200 square feet is the better deal.