Question

A) produce a regression equation to predict the selling prie for residences using a model of the following form: y1=B_{0 +} B₁ x_{1 +} b₂ X_{2 + e}

_{B) Interpert the parameters B1 and B2 in the model given in part a}

_{C) Produce an equation that describes the relationship between th selling price and the square footage of (1) condos and (2) single-family homes}

_{D) conduct a hypothesis test to determine if the relationship between the selling price and the square footage is different between condos and single-family homes}

Price ($)	Type	Square Feet	Price ($)	Type	Square feet
199,700	Family	1,500	200,600	condo	1,375
211,800	Condo	2,085	208,000	condo	1,825
197,100	Family	1,450	210,500	family	1,650
228,400	Family	1,836	233,300	family	1,960
215,800	Family	1,730	187,200	condo	1,360
190,900	Condo	1,726	185,200	condo	1,200
312,200	Family	2,300	284,100	family	2,000
313,600	Condo	1,650	207,200	family	1,755
239,000	Family	1,950	258,200	family	1,850
184,400	Condo	1,545	203,100	family	1,630

Answer 1

a)

We have modified the categorical data type in the below values ie 1 = Condo and 2 = Family

Running the regression on the modified data we get:

Regression Output

Regression Equation:

Selling Price = 62,371.82 + 90.37 * Square Feet + 3,629.50 * Type

b)

Coefficient of Square Feet

Value of 90.37 tells us the if we increase Square Feet by 1 units (keeps all the other variables constant), Value of Selling Price increases by 90.37 units.

Similarly, for Type

If we consider a Condo, then value of Selling Price increases by 3,629.50 units while for a 2 Family House, value of Selling Price increases by 2*3,629.50 units

c)

Regression Output with only Selling Price and Square foot variable:

Regression Equation:

Selling Price = 63,759.36 + 92.94 * Square feet

Regression Output with only Selling Price and Type foot variable:

Regression Equation:

Selling Price = 1,88,041.67 + 22,170.83* Type.

Note this model is insignificant as p-value from ANOVA table is more than 0.05.