A firm\'s operating costs can be classified as fixed, variable or mixed. Costs f
ID: 1218461 • Letter: A
Question
A firm's operating costs can be classified as fixed, variable or mixed. Costs for items such as telephone, electricity and maintenance are often mixed costs, meaning that they have both a fixed and variable cost component. A manufacturing firm has recorded its electricity costs in $ (Y) and the total number of hours of machine time in '000 hours (X) for each of 12 months and prepared the following summary data for the 12 months: Sum of all X values = 96 Sum of all Y values = 10,845 Sum of all X-squared values = 806 Sum of all Y-squared values = 9,964,025 Sum of all XY values = 89,130 Using the summary data provided, calculate the covariance and the coefficient of correlation between X and Y. What do these statistics tell you about the relationship between machine time (X) and the cost of electricity (Y)? Use the least squares method to derive a straight line relationship between X and Y. Explain how the least squares line coefficients can be interpreted in terms of fixed and variable costs of electricity.Explanation / Answer
a.)COV(X,Y)=E(XY)-E(X)E(Y)
E(XY)=89130/12=7427.5
E(X)=96/12=8
E(Y)=10845/12=903.75
COV(X,Y)=7427.5-8*903.75=197.5
sd(X)=sqrt((SUM[x^2] - SUM[x]^2 / n) / (n-1))=sqrt((806-(96/12)2)/12-1)=8.21
sd(Y)=sqrt((SUM[y^2] - SUM[y]^2 / n) / (n-1))=911.90
CORR(XY)=COV(XY)/sd(X)sd(Y)=197.5/8.21*911.90=.026
b)the above statistics shows a positive relationship between the two variable.Each variable is affected by the other and tend to move together in the same direction.
c)under least squares method,a liner relationship is established between x and y variable with the help of the equation
Y=a+bX
d)b=r.sd(x)/sd(y)
a=mean Y-b*meanX
where,Y=cost of electricity
x=machine hours
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