Mathematics, 30.05.2020 20:02 shadow29916

The plot shown below describes the relationship between the average income in a city and the average rent for a 111-bedroom apartment in that city.
Which of the following is the best estimate of the average change in rent associated with a \$5\text{,}000$5,000dollar sign, 5, start text, comma, end text, 000 increase in income?
Choose 1

Answers: 2

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Answer from: mags1467

The average change in rent can be determined by substituting the value of X as 5000 in the regression equation.

Step-by-step explanation:

A simple linear regression line is used to predict the value of the dependent variable from the independent variable.

The general form is:

$Y=\alpha +\beta X$

Dependent variables are those variables that are under study, i.e. they are being observed for any changes when the other variables in the model are changed.

The dependent variables are also known as response variables.

In this case the dependent variable is the average change in rent for a 1-bedroom apartment.

Independent variables are the variables that are being altered to see a proportionate change in the dependent variable. In a regression model there can be one or more than one independent variables.

The independent variables are also known as the predictor variables.

In this case the independent variable is the average income in a city.

So, for an increase of $5,000 in incomes the average change in rent can be determined by substituting the value of X as 5000 in the regression equation.

Answer from: Quest

a) justify

step-by-step explanation:

justifying is just part of everyday life. justify kind of means proof so i think the answer is a) justify.

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

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