Given the following data for four houses sold in comparable neighborhoods and their corresponding number of square feet, draw a scatter plot and find a linear regression equation representing a relationship between the number of square feet and the selling price of the house.

Question

Given the following data for four houses sold in comparable neighborhoods and their corresponding number of square feet, draw a scatter plot and find a linear regression equation representing a relationship between the number of square feet and the selling price of the house.

Square Feet

1528
2502
3004
3022
Selling Price

$94 comma 007
$228 comma 000
$250 comma 000
$271 comma 000
Question content area bottom
Part 1
Draw a scatter plot. Choose the correct graph below.
A.

x y graph
B.

x y graph
Your answer is correct.
C.

x y graph
Part 2
A linear regression equation is enter your response here
.
(Type an equation. Use integers or decimals for any numbers in the equation. Round to three decimal places as needed.)

Answer 1

Part 1: The correct graph is A.

Part 2: To find the linear regression equation, we can use the least squares method. First, let's organize the given data into two lists:

Square Feet: 1528, 2502, 3004, 3022
Selling Price: 94007, 228000, 250000, 271000

Now, let's calculate the mean of the square feet and the mean of the selling price:

Mean of square feet (x̄) = (1528 + 2502 + 3004 + 3022) / 4 = 2514
Mean of selling price (ȳ) = (94007 + 228000 + 250000 + 271000) / 4 = 212501.75

Next, let's calculate the deviations from the means for both lists:

x₁ - x̄ = 1528 - 2514 = -986
x₂ - x̄ = 2502 - 2514 = -12
x₃ - x̄ = 3004 - 2514 = 490
x₄ - x̄ = 3022 - 2514 = 508

ȳ₁ - ȳ = 94007 - 212501.75 = -118494.75
ȳ₂ - ȳ = 228000 - 212501.75 = 15498.25
ȳ₃ - ȳ = 250000 - 212501.75 = 37498.25
ȳ₄ - ȳ = 271000 - 212501.75 = 58498.25

Now, let's calculate the sum of the squares of the deviations for both lists:

∑(x - x̄)² = (-986)² + (-12)² + 490² + 508² = 639.0
∑(ȳ - ȳ)² = (-118494.75)² + 15498.25² + 37498.25² + 58498.25² = 2.145835004×10¹²

Finally, let's calculate the product of the deviations:

∑(x - x̄)(ȳ - ȳ) = (-986)(-118494.75) + (-12)(15498.25) + (490)(37498.25) + (508)(58498.25) = 7.502901011×10⁹

Now, we can find the slope (b) of the regression line:

b = ∑(x - x̄)(ȳ - ȳ) / ∑(x - x̄)² = (7.502901011×10⁹) / (639.0) = 11725.6902201

Next, let's find the intercept (a) of the regression line:

a = ȳ - b * x̄ = 212501.75 - (11725.6902201) * (2514) = -12394256.746

Therefore, the linear regression equation representing the relationship between the number of square feet and the selling price of the house is:

y = -12394256.746 + 11725.6902201 * x

Given the following data for four houses sold in comparable neighborhoods and their corresponding number of square​ feet, draw a scatter plot and find a linear regression equation representing a relationship between the number of square feet and the selling price of the house.

Part 1: The correct graph is A.

Given the following data for four houses sold in comparable neighborhoods and their corresponding number of square feet, draw a scatter plot and find a linear regression equation representing a relationship between the number of square feet and the selling price of the house.