Mathematics, 07.03.2020 04:29 Tnguyen8160

An economist is studying the job market in Denver area neighborhoods. Let x represent the total number of jobs in a given neighborhood, and let y represent the number of entry-level jobs in the same neighborhood. A sample of six Denver neighborhoods gave the following information (units in hundreds of jobs).

x 13 34 52 28 50 25

y 1 4 5 5 9 3

Complete parts (a) through (e), given Σx = 202, Σy = 27, Σx2 = 7938, Σy2 = 157, Σxy = 1074, and r ≈ 0.821.
a. Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r.
b. Find x, and y. Then find the equation of the least-squares line y = a + bx. (Round your answers for x and yto two decimal places. Round your answers for a and b to three decimal places.)
c. Find the value of the coefficient of determination r2. What percentage of the variation in y can be explainedby the corresponding variation in x and the least-squares line?
d. For a neighborhood with x = 34 hundred jobs, how many are predicted to be entry level jobs?

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Answer from: Carlos448

a) $\sum X = 13+34+52+28+50+25 =202$

$\sum Y = 1+4+5+5+9+3= 27$

$\sum X^2 = 13^2+34^2+52^2+28^2+50^2+25^2 = 1074$

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

$r=\frac{6(1074)-(202)(27)}{\sqrt{[6(7938) -(202)^2][6(157) -(202)^2]}}=0.821$

b) $m=\frac{165}{1137.33}=0.145$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{202}{6}=33.67$

$\bar y= \frac{\sum y_i}{n}=\frac{27}{6}=4.5$

And we can find the intercept using this:

$b=\bar y -m \bar x=4.5-(0.145*33.67)=-0.384$

So the line would be given by:

y=0.145 x -0.384

c) The coefficient of variation is given by:

r^2 = 0.821^2 = 0.674

And we can conclude that 67.4% of the variation in y can be explainedby the corresponding variation in x and the least-squares line

d) For this case we just need to replade x = 34 into our model and we got:

y=0.145*34 -0.384= 3.097

Step-by-step explanation:

For this case we have the following data:

x 13 34 52 28 50 25

y 1 4 5 5 9 3

Part a

$\sum X = 13+34+52+28+50+25 =202$

$\sum Y = 1+4+5+5+9+3= 27$

$\sum X^2 = 13^2+34^2+52^2+28^2+50^2+25^2 = 1074$

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

$r=\frac{6(1074)-(202)(27)}{\sqrt{[6(7938) -(202)^2][6(157) -(202)^2]}}=0.821$

Part b

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=7938-\frac{202^2}{6}=1137.33$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=1074-\frac{202*27}{6}=165$

And the slope would be:

$m=\frac{165}{1137.33}=0.145$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{202}{6}=33.67$

$\bar y= \frac{\sum y_i}{n}=\frac{27}{6}=4.5$

And we can find the intercept using this:

$b=\bar y -m \bar x=4.5-(0.145*33.67)=-0.384$

So the line would be given by:

y=0.145 x -0.384

Part c

The coefficient of variation is given by:

r^2 = 0.821^2 = 0.674

And we can conclude that 67.4% of the variation in y can be explainedby the corresponding variation in x and the least-squares line

Part d

For this case we just need to replade x = 34 into our model and we got:

y=0.145*34 -0.384= 3.097

Answer from: Quest

dont think so

step-by-step explanation:

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

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