Question: (20) An economist complied 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 year (Low, Moderate, High). The results of the study follow (productivity improvement is measured on a scale from 0 to 100).

1. What is the response variable? What is the factor, and how many levels of the factor has? Make aligned dot plots of the data. Explain the dot plots. (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?)
2. Test whether or not the mean productivity improvement differs according to the level of research and development expenditures. Use = 0.05. What the statistical method are you going to use for data? Write down your statistical model, state the null and alternative hypothesis, decision rule, and make the conclusions. If the null hypothesis is rejected, please conduct the multiple comparisons to further tell the mean differences.
3. Obtain the fitted values.
4. Obtain the residuals plot and check the assumptions of your statistical method.
5. Fit a linear regression model and interpret the coefficients in the model in the context of problem.
6. What appears to be the nature of the relationship between research and development expenditures and productivity improvement?

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