Part I. The Baker Company wants to develop a budget to predict how overhead costs vary with activity levels. Management is trying to decide whether direct labor hours (DLH) or the number of units produced (Units) is the better measure of activity for the firm. Monthly data for the preceding 24 months appears below (and in the posted file). Use regression analysis to determine which measure, DLH or Units should be used for the budget
1.Determine if each model is a valid use of regression. (Straight line?, relationship?, assumptions ?)
2. Select the best model. For that model:
a)Write the regression equation (i.e. what are the values of b0 and b1)
b)Interpret the meaning of the slope b1 in this problem.
c)Estimate the average overhead using your X variable (either DLH = 1,300 or Units = 140).
d)Determine the value of the coefficient of determination and interpret its meaning.
e)Find the standard error of the estimate
f)At the 1% level of significance is there a relationship
g) Set up a 95% confidence interval of the slope β1.
h) Set up a 95% confidence interval for the actual overhead in one month given the x value in “c.”.
Part II. In the 1994 congressional election, the Republican candidate outpolled the Democratic candidate by 400 votes (excluding absentee ballots). The Democratic candidate outpolled the Republican candidate by 500 absentee votes. The Republican candidate sued (and won), claiming that vote fraud must have played a role in the absentee ballot count. The Republican’s lawyer ran a regression to predict (based on past elections) how the absentee ballot margin could be predicted from the votes tabulated on voting machines. Selected results are given. Show how this regression could be used by the Republican to prove his claim of vote fraud. (Hint: Is the 1994 result an outlier? Consider using a confidence interval.)
Year
Voting machine margin (x)
Absentee ballot margin (y)
1976
800
85
1978
600
65
1980
-200
-30
1982
100
13
1984
120
11
1986
-300
-28
1988
-700
-73
1990
600
66
1992
-380
-42
