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Regression Basics

In: Business and Management

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Size 850 1450 1085 1232 718 1485 1136 726 700 956 1100 1285 1985 1369 1175 1225 1245 1259 1150 896 1361 1040 755 1000 1200 Rent 950 1600 1200 1500 950 1700 1650 935 875 1150 1400 1650 2300 1800 1400 1450 1100 1700 1200 1150 1600 1650 1200 800 1750

A real estate company in downtown Miami 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 in a particular residential neighborhood was chosen. Q-2a: Construct a scatter plot of rent/size. Q-2b: Find the equation of the least squares regression line that models the relationship between square footage and rental amount and interpret the meaning of the coefficients. Q-2c: Predict the monthly rent for an apartment with 1000 square feet. Q-2d: Explain why it would not be appropriate to use the model to predict the monthly rent for apartments that have 500 square feet. Q-2e: You are considering signing a lease for an apartment in this residential neighborhood. You are deciding between two apartments, one with 1,000 square feet that rents for $1,275 and the other with 1,200 square fee that rents for $1,425. Which is a better deal? Explain.

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Q-2a

Rent vs. Size
2500 2000 Rent in $ 1500 1000 500 0 0 500 1000 1500 2000 2500 Size in sq. feet y = 1.0651x + 177.12 R² = 0.7226

Q-2b Regression equation = (slope) (x) + (y-intercept) = (1.0651) (x) + (177.12) The slope is 1.0651. This means the rent increases by $1.07 for every sq. foot increase in size Q-2c Regression equation = (slope) (x) + (y-intercept) = (1.0651) (1000) + (177.12) = $1,242.22 According to the data provided, the monthly rent for a 1,000 square feet is $1,242.22 Q-2d

It would not be appropriate to use the model to predict the monthly rent for apartments that have 500 square feet because the smallest apartment...

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