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?

a)

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

b)  

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

And we can find the intercept using this:  

So the line would be given by:  

c) The coefficient of variation is given by:

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:

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

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

Part b

Where:  

With these we can find the sums:  

And the slope would be:  

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

And we can find the intercept using this:  

So the line would be given by:  

Part c

The coefficient of variation is given by:

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: