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ID: 3259172 • Letter: H
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home / study / math / statistics and probability / questions and answers / 2. the credit union at united university has a ... Your question has been answered Let us know if you got a helpful answer. Rate this answer Question: 2. The credit union at United University has a lar... 2. The credit union at United University has a large number of members who make deposits to their accounts via a payroll deduction plan. A sample of 50 such members yields the following information/data: Y = amount of payroll deductions (hundreds of dollars) X = annual salary (hundreds of dollars) Y = -2 + 0.05 X SSE = 6 SS(total) = 20 X ranges from 70 to 140 SSXX = 4800 X bar = 100 a. Calculate the MSE. b. Interpret the estimated slope coefficient. c. At the 1% level of significance, test whether or not the population slope coefficient equals 0 or not. d. Construct the appropriate ANOVA table for this regression setting. e. Compute the sample coefficient of correlation. f. Compute the coefficient of determination. g. Predict the amount of payroll deduction for an individual who earns $12,000 in a year. (5 pts)
Explanation / Answer
here Y=a+bx=-2+0.05X
(1) MSE=SSE/df(E)=6/48=0.125
(2) slope coefficient is unit change in Y with X.
here slope=0.05 so when one unit X is increased then 0.05 unit of Y will increase and vice-versa
(3) SE(b)=Se/Sqrt(SSXX)=0.3535/sqrt(4800)=0.0051
Se=sqrt(MSE)=sqrt(0.125)=0.3536
t=b/SE(b)=0.05/0.0051=9.8 with error df=n-2=48
critical t(0.01,48)=2.68 is less than calculated t=9.8 so slope coefficient is not equal to 0
(4)
(5)correlation coefficient=r=sqrt(R2)=0.8367
(6)coefficient of determination=R2= SS(regression)/SS(total)=14/20=0.7
(7)here X=120 hunderd, so Y=-2+0.05*120=4
Anova source df ss ms f regression 1 14 14 112 error 48 6 0.125 total 49 20Related Questions
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