Question

Sanchez & Wright, a research firm for the real estate industry, studied the relation between x=x= annual income (in thousands of dollars) and y=y= sale price of house purchased (in thousands of dollars). A random sample of data was collected from mortgage applications for home sales in the region of the study, and is given in the table.

Annual Income House Price
103 164.5
105 259
101 197.9
81 188.2
89 166.2
68 164.4
48 106.8
55 139
79 166


Conduct a linear regression. Use the results to answer the following questions.
if a buyer's annual income increases by $1000, the model's predicted change in dollars of the sale price of the house they will purchase is:

Answer 1

If a buyer's annual income increases by $1000, the model's predicted change in dollars of the sale price of the house they will purchase is $1636.41

How to solve for the predicted value

The values from the table calculation are

Total 729 1552 62511 281658 131227

Sum of X = 729

Sum of Y = 1552

Mean X = 81

Mean Y = 172.4444

Sum of squares (SSX) = 3462

Sum of products (SP) = 5515

Regression Equation = ŷ = bX + a

b = SP/SSX = 5515/3462 = 1.59301

a = MY - bMX = 172.44 - (1.59*81) = 43.41065

ŷ = 1.59301X + 43.41065

The regression equation is y = 1.59301X + 43.41065

when x = 1000 dollars we have

y = 1.59301 * 1000 + 43.41065

= $1595 + 43.41

= $1636.41