COSS SENSE-MAKING The sides of square ABCD are extended

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:

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