Question

For the response variable​ y, the selling price in thousands of​ dollars, and the expanatory variable​ x, the size of the house in thousands of square​ feet, ModifyingAbove y with caretequals9.4plus76.7x. a. How much do you predict a house would sell for if it has​ (i) 2000 square​ feet, (ii) 3000 square​ feet? b. Using results in part​ a, explain how to interpret the slope.c. Is the correlation between these variables positive or​ negative? Why?d. One home that is 3000 square feet sold for​ $300,000. Find the​ residual, and interpret.

Answer 1

Answer:

a) i) 162.8 thousand dollars, ii) 239.5 thousand dollars

b) m = 76.7

c) Positive

d) Positive residual          

Step-by-step explanation:

We are given the following in the question:

The selling price is the response variable given by the equation:

$y = 9.4 + 76.7x$

where y is in thousands of​ dollars and x is in thousands of square​ feet.

a) Predicted selling price

i) 2000 square​ feet

We put x = 2

$y = 9.4 + 76.7(2)\\y =162.8$

Thus, the selling prices is 162.8 thousand dollars.

i) 3000 square​ feet

We put x = 3

$y = 9.4 + 76.7(3)\\y =239.5$

Thus, the selling prices is 239.5 thousand dollars.

b) Interpretation of slope

Comparing to general equation:

$y = mx + c$

Slope, m = 76.7

Thus, with increase in 1 unit of x that is one thousand square feet, the selling price of the house increases by 76.7 thousand dollars.

c)  correlation between variables

Since the slope between the two variables is positive, the correlation between the variable, selling price of the house and the size of the house is positive.

d) House size = 3000 square feet

Actual selling price = $300,000

Predicted selling price = $239,500

Residual:

R = Actual - Predicted

$R = 300-239.5= 60.5$

Interpretation:

Since the residual is positive, thus, the selling price is above the average price.