Question

Question 12 [15 Points] Show proper work. Topic: Linear regression The following data represents the number of full-time employees (x) and the number of job openings postedly) for the top 10 hospitals in Boston metro area (Source: Boston Medical Journal 2009). 2450 3900 9600 9900 13235 1900 5530 6700 7785 4300 210 280 490 565 625 175 435 420 680 350 Consider the following: Exy - 32,536,925 Ex544,958,625 Zyl. 2,053,600 Ex-_65,315 Ey - 4,230 PLEASE DO DETAILED WORK IN THE NEXT PAGE. a) X - b) Draw the scatter plot (diagram). c) Does there appear to be a linear relationship just based on the scatter diagram? d) Find the equation of the best fit line based on the data given. Y(number of openings) e) Now draw the line on the scatter diagram to the right. f) Discuss if there are outliers and / or influential point(s). X (Number of employees) g) Estimate the number of job openings at a certain hospital in the same metro area, if the total number of employees in that hospital is 4900. h) Find the coefficient of determination (r) and interpret its value. PLEASE DO THE CALCULATIONS IN THE NEXT PAGE, NOT ON THIS PAGE. 12

Answer 1

A)

sample size ,   n =   10      
here, x̅ = Σx / n=   6530.00   ,     ȳ = Σy/n =   423.00

B)

Scatterplot 0 2 000 4000 6000 8000 10000 12000 14000

C)

RELATION APPEAR TO BE LINEAR AND POSITVE

D)

estimated slope , ß1 = SSxy/SSxx =   4904825.0   /   118315850.000   =   0.0415
                  
intercept,   ß0 = y̅-ß1* x̄ =   152.2966          
                  
so, regression line is   Ŷ =   152.2966   +   0.0415   *x

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E)

Scatterplot 2000 4000 6000 8 000 10000 12000 14000

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G)

Predicted Y at X=   4900   is                  
Ŷ =   152.29656   +   0.041455   *   4900   =   355.428

...............

H)

R² =    (Sxy)²/(Sx.Sy) =    0.7693
76.93% OF VARIATION CAN BE EXPLAINED BY X

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