Round your answer to the nearest hundredth.

An economist is studying the job market in Denver area neighborhoods. Let x represent the total number of jobs in a given neighb

Troyanec [42]

Answer:

The sample correlation coefficient is, r = 0.8722.

The equation of the least-squares line is:

$y= -0.161+0.154x$

Step-by-step explanation:

(a)

The scatter diagram displaying the data for X : total number of jobs in a given neighborhood and Y : number of entry-level jobs in the same neighborhood is shown below.

(b)

The table attached below verifies the values of $\sum X,\ \sum Y,\ \sum X^{2},\ \sum Y^{2}\ \text{and}\ \sum XY$ .

The sample correlation coefficient is:

$\begin{aligned}r~&=~\frac{n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}} {\sqrt{\left[n \sum{X^2}-\left(\sum{X}\right)^2\right] \cdot \left[n \sum{Y^2}-\left(\sum{Y}\right)^2\right]}} \\r~&=~\frac{ 6 \cdot 1163 - 201 \cdot 30 } {\sqrt{\left[ 6 \cdot 7759 - 201^2 \right] \cdot \left[ 6 \cdot 182 - 30^2 \right] }} \approx 0.8722\end{aligned}$

Thus, the sample correlation coefficient is, r = 0.8722.

(c)

The slope and intercept are:

$\begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 30 \cdot 7759 - 201 \cdot 1163}{ 6 \cdot 7759 - 201^2} \approx -0.161 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 6 \cdot 1163 - 201 \cdot 30 }{ 6 \cdot 7759 - \left( 201 \right)^2} \approx 0.154\end{aligned}$

The equation of the least-squares line is:

$y= -0.161+0.154x$

(d)

The least-squares line is graphed in the diagram below.

6 0

3 years ago

One tank is filling at a rate of

jeka57 [31]

Answer:

The answer is the 59 gallons per 13 minutes.

Step-by-step explanation:

the first tank is filling at a rate of 175 gallons per hour because 60/12 is 5 and 35*5 is 175. the second tank is filling at a rate of 272.3 gallons per hour because 60/13 is 4.6 and 59*4.6 is 272.3

4 0

3 years ago

Solve the inequality for u -5u+27 [less than or equal to] 2

baherus [9]

Answer:

5≤u

Step-by-step explanation:

Put the words and numbers into an equation:

-5u+27≤2

Put all like terms on one side:

27-2≤5u ---> Do you see what I did there? Now you don't have to work with negatives. :)

Simplify:

25≤5u

Solve:

5≤u

:)

6 0

3 years ago

A number is greater than another number by 5. if their sum is 21, find the number. give full step

Licemer1 [7]

Step-by-step explanation:

given that

let thenumber be x greater than 5

x 5 plus 21

x 26

7 0

3 years ago

Lots of equations that equal 420? Anybody know some?

creativ13 [48]

If we do it algebraically, we get

x + y = 420

This is the simplest equation. You see now this is a linear pair in two variables. Thus, there will be infinitely many solutions.

E.g - 419 + 1 = 420

42 * 10 = 420
21 * 20 = 420

etc,....

4 0

3 years ago

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