Answer :
Sure, I'd be happy to help with this!
Part (a): Calculate the Monthly Rent
We are given a linear regression equation that relates the square footage [tex]\( x \)[/tex] of an apartment to the monthly rental price [tex]\( y \)[/tex]:
[tex]\[
y = 1.165x + 615.23
\][/tex]
To find the monthly rent for an apartment with 1,500 square feet, we substitute [tex]\( x = 1500 \)[/tex] into the equation:
[tex]\[
y = 1.165(1500) + 615.23
\][/tex]
When you do the computation, you'll get:
- [tex]\( 1.165 \times 1500 = 1747.5 \)[/tex]
- Adding the constant: [tex]\( 1747.5 + 615.23 = 2362.73 \)[/tex]
So, the monthly rent for a 1,500 square foot apartment is approximately \[tex]$2,362.73.
Part (b): Determine if Jacob Can Afford the Rent
Jacob makes $[/tex]8,000 per month, and we need to determine if he can afford this rent based on the recommendation that no more than 28% of his monthly gross income should go towards housing.
First, calculate 28% of Jacob's monthly income:
[tex]\[
\text{Max affordable rent} = 0.28 \times 8000 = 2240
\][/tex]
So Jacob should not spend more than \[tex]$2,240 on rent each month.
Since the calculated rent of \$[/tex]2,362.73 exceeds \$2,240, Jacob cannot afford the apartment, as the rent is more than 28% of his monthly income.
I hope this breakdown helps! If you have any more questions, feel free to ask.
Part (a): Calculate the Monthly Rent
We are given a linear regression equation that relates the square footage [tex]\( x \)[/tex] of an apartment to the monthly rental price [tex]\( y \)[/tex]:
[tex]\[
y = 1.165x + 615.23
\][/tex]
To find the monthly rent for an apartment with 1,500 square feet, we substitute [tex]\( x = 1500 \)[/tex] into the equation:
[tex]\[
y = 1.165(1500) + 615.23
\][/tex]
When you do the computation, you'll get:
- [tex]\( 1.165 \times 1500 = 1747.5 \)[/tex]
- Adding the constant: [tex]\( 1747.5 + 615.23 = 2362.73 \)[/tex]
So, the monthly rent for a 1,500 square foot apartment is approximately \[tex]$2,362.73.
Part (b): Determine if Jacob Can Afford the Rent
Jacob makes $[/tex]8,000 per month, and we need to determine if he can afford this rent based on the recommendation that no more than 28% of his monthly gross income should go towards housing.
First, calculate 28% of Jacob's monthly income:
[tex]\[
\text{Max affordable rent} = 0.28 \times 8000 = 2240
\][/tex]
So Jacob should not spend more than \[tex]$2,240 on rent each month.
Since the calculated rent of \$[/tex]2,362.73 exceeds \$2,240, Jacob cannot afford the apartment, as the rent is more than 28% of his monthly income.
I hope this breakdown helps! If you have any more questions, feel free to ask.
