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Annie Stevens PMBA 6331 Problem Set 3   Q1

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Annie Stevens

PMBA 6331 Problem Set 3

 

Q1.  An accountant wishes to predict labor cost (y) on the basis of batch size (x) of a product produced in a job shop.  Data for 12 production runs include

Direct labor cost	Batch size
71	5
663	62
381	35
138	12
861	83
145	14
493	46
548	52
251	23
1024	100
435	41
772	1

 

Construct a scatter plot of y versus x.

Does the scatter plot suggest that a simple linear regression model might be appropriate?  Before moving on, address any concerns?

Q2.  Use the data in Q1 to estimate a simple linear regression model.

What are the values of the intercept and slope coefficients?  Interpret the meanings of b0 and b1.

Write the least squares prediction equation.

Use the least squares line to obtain a point estimate of the mean direct labor costs for all batches of size 60 and a point prediction of the direct labor cost for an individual batch of size 60.

Q3.  Set up the appropriate null and alternative hypotheses to determine whether labor is statistically significantly related to batch size.  What is the calculated t-statistic?  What is the critical t-statistic?  What is the p-value?  Use these results to determine whether you reject or fail to reject the null hypothesis that there is no effect using a significance level of .05.

Q4. Use your results to solve for and interpret the following:

What is the point estimate of the mean square error σ2?

What is the point estimate of the standard error σ?

Interpret the confidence interval for the slope coefficient.  How can we use this information to determine whether we should reject or fail to reject the null hypothesis that there is no effect?

What is the coefficient of determination?

Finally, is the “model” statistically significant based on the F-test?

Q5.  Refer to the attached “stocks” data.  Data include NYSE index values, GDP measured in billions of dollars, and time from 1980-2006.  First, estimate the following equation using Ordinary Least Squares (OLS):

1. Use a scatter diagram to assess whether there is first-order autocorrelation in this series?
2. Now, assess whether there is first-order autocorrelation based on the basis of the d test.  Note: use the command “tsset time” so that you can estimate the Durbin-Watson statistic using “estat dwatson.”