How do i calculate g on calculate g A sociologist is interested in the relation between x = number of job changes and y = annual salary (in thousands of dollars) for people living in the Nashville area. A random sample of 10 people employed in Nashville provided the following information. x (number of job changes) 4 5 6 6 1 5 9 10 10 3 y (Salary in $1000) 37 34 32 32 32 38 43 37 40 33 In this setting we have Σx = 59, Σy = 358, Σx2 = 429, Σy2 = 12,948, and Σxy = 2180. (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to four decimal places.) x = y = b = ŷ = + x (b) Draw a scatter diagram displaying the data. Graph the least-squares line on your scatter diagram. Be sure to plot the point (x, y). (c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.) r = r2 = What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.) %(d) Test the claim that the population correlation coefficient ρ is positive at the 5% level of significance. (Round your test statistic to three decimal places.) t = Find or estimate the P-value of the test statistic. P-value > 0.2500.125 < P-value < 0.250 0.100 < P-value < 0.1250.075 < P-value < 0.1000.050 < P-value < 0.0750.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.0100.0005 < P-value < 0.005P-value < 0.0005 Conclusion Reject the null hypothesis. There is sufficient evidence that ρ > 0.Reject the null hypothesis. There is insufficient evidence that ρ > 0. Fail to reject the null hypothesis. There is sufficient evidence that ρ > 0.Fail to reject the null hypothesis. There is insufficient evidence that ρ > 0. (e) If someone had x = 10 job changes, what does the least-squares line predict for y, the annual salary? (Round your answer to two decimal places.) thousand dollars(f) Find Se. (Round your answer to two decimal places.)Se = (g) Find a 90% confidence interval for the annual salary of an individual with x = 10 job changes. (Round your answers to two decimal places.) lower limit thousand dollars upper limit thousand dollars (h) Test the claim that the slope β of the population least-squares line is positive at the 5% level of significance. (Round your test statistic to three decimal places.) t = Find or estimate the P-value of the test statistic. P-value > 0.2500.125 < P-value < 0.250 0.100 < P-value < 0.1250.075 < P-value < 0.1000.050 < P-value < 0.0750.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.0100.0005 < P-value < 0.005P-value < 0.0005

How do i calculate g on calculate g A sociologist is interested in the relation between x = number of job changes and y = annual salary (in thousands of dollars) for people living in the Nashville area. A random sample of 10 people employed in Nashville provided the following information. x (number of job changes) 4 5 6 6 1 5 9 10 10 3 y (Salary in $1000) 37 34 32 32 32 38 43 37 40 33 In this setting we have Σx = 59, Σy = 358, Σx2 = 429, Σy2 = 12,948, and Σxy = 2180. (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to four decimal places.) x = y = b = ŷ = + x (b) Draw a scatter diagram displaying the data. Graph the least-squares line on your scatter diagram. Be sure to plot the point (x, y). (c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.) r = r2 = What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.) %(d) Test the claim that the population correlation coefficient ρ is positive at the 5% level of significance. (Round your test statistic to three decimal places.) t = Find or estimate the P-value of the test statistic. P-value > 0.2500.125 < P-value < 0.250 0.100 < P-value < 0.1250.075 < P-value < 0.1000.050 < P-value < 0.0750.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.0100.0005 < P-value < 0.005P-value < 0.0005 Conclusion Reject the null hypothesis. There is sufficient evidence that ρ > 0.Reject the null hypothesis. There is insufficient evidence that ρ > 0. Fail to reject the null hypothesis. There is sufficient evidence that ρ > 0.Fail to reject the null hypothesis. There is insufficient evidence that ρ > 0. (e) If someone had x = 10 job changes, what does the least-squares line predict for y, the annual salary? (Round your answer to two decimal places.) thousand dollars(f) Find Se. (Round your answer to two decimal places.)Se = (g) Find a 90% confidence interval for the annual salary of an individual with x = 10 job changes. (Round your answers to two decimal places.) lower limit thousand dollars upper limit thousand dollars (h) Test the claim that the slope β of the population least-squares line is positive at the 5% level of significance. (Round your test statistic to three decimal places.) t = Find or estimate the P-value of the test statistic. P-value > 0.2500.125 < P-value < 0.250 0.100 < P-value < 0.1250.075 < P-value < 0.1000.050 < P-value < 0.0750.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.0100.0005 < P-value < 0.005P-value < 0.0005

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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How do i calculate g on calculate g

A sociologist is interested in the relation between x = number of job changes and y = annual salary (in thousands of dollars) for people living in the Nashville area. A random sample of 10 people employed in Nashville provided the following information.

x _{(number of job changes)}	4	5	6	6	1	5	9	10	10	3
y _{(Salary in $1000)}	37	34	32	32	32	38	43	37	40	33

In this setting we have Σx = 59, Σy = 358, Σx² = 429, Σy² = 12,948, and Σxy = 2180.

(a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to four decimal places.)

x	=
y	=
b	=
ŷ	=	+ x

(b) Draw a scatter diagram displaying the data. Graph the least-squares line on your scatter diagram. Be sure to plot the point (x, y).

(c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.)

r =
r² =

What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)
%

(d) Test the claim that the population correlation coefficient ρ is positive at the 5% level of significance. (Round your test statistic to three decimal places.)

t =

Find or estimate the P-value of the test statistic.

P-value > 0.2500.125 < P-value < 0.250 0.100 < P-value < 0.1250.075 < P-value < 0.1000.050 < P-value < 0.0750.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.0100.0005 < P-value < 0.005P-value < 0.0005

Conclusion

Reject the null hypothesis. There is sufficient evidence that ρ > 0.Reject the null hypothesis. There is insufficient evidence that ρ > 0. Fail to reject the null hypothesis. There is sufficient evidence that ρ > 0.Fail to reject the null hypothesis. There is insufficient evidence that ρ > 0.

(e) If someone had x = 10 job changes, what does the least-squares line predict for y, the annual salary? (Round your answer to two decimal places.)
thousand dollars

(f) Find S_e. (Round your answer to two decimal places.)
S_e =

(g) Find a 90% confidence interval for the annual salary of an individual with x = 10 job changes. (Round your answers to two decimal places.)

lower limit	thousand dollars
upper limit	thousand dollars

(h) Test the claim that the slope β of the population least-squares line is positive at the 5% level of significance. (Round your test statistic to three decimal places.)

t =

Find or estimate the P-value of the test statistic.

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