Answer :
To find the monthly rent for an apartment with 1,500 square feet using the given linear regression equation [tex]\( y = 1.165x + 615.23 \)[/tex], follow these steps:
1. Understand the equation: In this equation, [tex]\( x \)[/tex] represents the square footage of the apartment, and [tex]\( y \)[/tex] represents the monthly rental price. The equation is of the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
2. Substitute the value of [tex]\( x \)[/tex]: To find the monthly rent for an apartment that has 1,500 square feet, substitute [tex]\( x = 1500 \)[/tex] into the equation.
3. Calculate:
- Multiply the slope by the square footage: [tex]\( 1.165 \times 1500 \)[/tex].
- Add the intercept: [tex]\((1.165 \times 1500) + 615.23\)[/tex].
4. Perform the multiplication:
- First, calculate [tex]\( 1.165 \times 1500 = 1747.5 \)[/tex].
5. Add the intercept:
- Then, add 615.23 to 1747.5, which equals 2362.73.
Therefore, the monthly rent for an apartment with 1,500 square feet is $2,362.73.
1. Understand the equation: In this equation, [tex]\( x \)[/tex] represents the square footage of the apartment, and [tex]\( y \)[/tex] represents the monthly rental price. The equation is of the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
2. Substitute the value of [tex]\( x \)[/tex]: To find the monthly rent for an apartment that has 1,500 square feet, substitute [tex]\( x = 1500 \)[/tex] into the equation.
3. Calculate:
- Multiply the slope by the square footage: [tex]\( 1.165 \times 1500 \)[/tex].
- Add the intercept: [tex]\((1.165 \times 1500) + 615.23\)[/tex].
4. Perform the multiplication:
- First, calculate [tex]\( 1.165 \times 1500 = 1747.5 \)[/tex].
5. Add the intercept:
- Then, add 615.23 to 1747.5, which equals 2362.73.
Therefore, the monthly rent for an apartment with 1,500 square feet is $2,362.73.