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Answer :
We are given the linear regression equation
[tex]$$
y = 1.165x + 615.23,
$$[/tex]
where [tex]$x$[/tex] is the square footage and [tex]$y$[/tex] is the monthly rental price.
Step 1. Estimate the monthly rent.
For an apartment with 1,500 square feet, substitute [tex]$x = 1500$[/tex] into the equation:
[tex]$$
y = 1.165(1500) + 615.23.
$$[/tex]
Calculating the product:
[tex]$$
1.165 \times 1500 = 1747.5.
$$[/tex]
Then, add the intercept:
[tex]$$
1747.5 + 615.23 = 2362.73.
$$[/tex]
Thus, the monthly rent is \[tex]$2362.73.
Step 2. Determine the maximum housing expense for Jacob.
It is recommended that no more than $[/tex]28\%[tex]$ of the monthly gross income be spent on housing. Jacob's monthly income is \$[/tex]8,000, so:
[tex]$$
\text{Maximum housing expense} = 0.28 \times 8000 = 2240.
$$[/tex]
Step 3. Compare the rent with the maximum allowable expense.
Since
[tex]$$
2362.73 > 2240,
$$[/tex]
the monthly rent of \[tex]$2362.73 exceeds the maximum recommended housing expense of \$[/tex]2240.
Conclusion:
a. The monthly rent for an apartment with 1,500 square feet is \$2362.73.
b. Jacob cannot afford this rental because the rent is more than 28% of his monthly income.
[tex]$$
y = 1.165x + 615.23,
$$[/tex]
where [tex]$x$[/tex] is the square footage and [tex]$y$[/tex] is the monthly rental price.
Step 1. Estimate the monthly rent.
For an apartment with 1,500 square feet, substitute [tex]$x = 1500$[/tex] into the equation:
[tex]$$
y = 1.165(1500) + 615.23.
$$[/tex]
Calculating the product:
[tex]$$
1.165 \times 1500 = 1747.5.
$$[/tex]
Then, add the intercept:
[tex]$$
1747.5 + 615.23 = 2362.73.
$$[/tex]
Thus, the monthly rent is \[tex]$2362.73.
Step 2. Determine the maximum housing expense for Jacob.
It is recommended that no more than $[/tex]28\%[tex]$ of the monthly gross income be spent on housing. Jacob's monthly income is \$[/tex]8,000, so:
[tex]$$
\text{Maximum housing expense} = 0.28 \times 8000 = 2240.
$$[/tex]
Step 3. Compare the rent with the maximum allowable expense.
Since
[tex]$$
2362.73 > 2240,
$$[/tex]
the monthly rent of \[tex]$2362.73 exceeds the maximum recommended housing expense of \$[/tex]2240.
Conclusion:
a. The monthly rent for an apartment with 1,500 square feet is \$2362.73.
b. Jacob cannot afford this rental because the rent is more than 28% of his monthly income.
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