Reference no: EM131096168
Refer to Productivity improvement Problem 16.7. The economist also has information on annual productivity improvement in the prior year and wishes to use this information as a concomitant variable. The data on the prior year's productivity improvement (Xij) follow.
a. Obtain the residuals for covariance model (22.3).
b. For each treatment, plot the residuals against the fitted values. Also prepare a normal probability plot of the residuals and calculate the coefficient of correlation between the ordered residuals and their expected values under normality. What do you conclude from your analysis?
c. State the generalized regression model to be employed for testing whether or not the treatment regression lines have the same slope. Conduct this test using α = .01. State the alternatives, decision rule, and conclusion. What is the P-value of the test?
d. Could you conduct a formal test here as to whether the regression functions are linear? If so, how many degrees of freedom are there for the denominator mean square in the test statistic?
Problem 16.7
Productivity improvement. An economist compiled data on productivity improvements last year for a sample of firms producing electronic computing equipment. The firms were classified according to the level of their average expenditures for research and development in the past three years (low, moderate, high). The results of the study follow (productivity improvement is measured on a scale from a to 100). Assume that ANOVA model (16.2) is appropriate.
a. Prepare aligned dot plots of the data. Do the factor level means appear to differ? Does the variability of the observations within each factor level appear to be approximately the same for all factor levels?
b. Obtain the fitted values.
c. Obtain the residuals. Do they sum to zero in accord with (16.21)?
d. Obtain the analysis of variance table.
e. Test whether or not the mean productivity improvement differs according to the level of research and development expenditures. Control the α risk at .05. State the alternatives, decision rule, and conclusion.
f. What is the P-value of the test in part (e)? How does it support the conclusion reached in part (e)? g. What appears to be the nature of the relationship between research and development expenditures and productivity improvement?
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