1. A Statistical Analysis Example of A Full Functional Utilization of An Engineering Calculator Li-Fei Huang (lhuang@mcu.edu.tw) Dept. of App. Statistics & Info. Sci. Ming Chuan University, TAIWAN

2. Outline Introduction Steps of simple linear regression analysis Commands for programming Regression test program Execution result Conclusions References

3. Introduction The functions and commands of statistical software which is installed in the computer are quite COMPLICATED. The engineering calculator is EASIER to manipulate and CHEAPER to possess. Today even the PROGRAMMING can be done. This paper will use CASIO fx-7400G PLUS to do the simple linear regression analysis.

4. CASIO fx-7400G PLUS The slope, the intercept and the coefficient of correlation are shown directly. There are NO further results about hypothesis testing. Lots of basic statistics such as can be extracted from the memory of the calculator to create the program about hypothesis testing.

5. Simple linear regression (Step 1) The sum of squares for X: The slope for the regression line: The intercept for the regression line:

6. Simple linear regression (Step 2) The sum of squares for regression: The sum of squares for Y or the sum of squares for total: The sum of squares for error: The mean squares for error: The regression F test value:

7. Simple linear regression (Step 3) The coefficient of determination: The coefficient of correlation: if X and Y are positively correlated, if X and Y are negatively correlated.

8. Simple linear regression (Step 4) The t tests for the slope and the intercept: The confidence interval and the prediction interval for a given value of X:

9. Commands for programming Parts of commands from CASIO fx-7400G PLUS manual:

10. Regression test program (Step1)

11. Regression test program (Step2)

12. Regression test program (Step3)

13. Regression test program (Step4) The t tests for the slope and the intercept:

14. Regression test program (Step4) The SE parts of the confidence interval and the prediction interval for a given value of X:

15. Execution result One data set in the book of Berenson, Levine, & Krehbiel

16. Execution result (Step 2)

17. Execution result (Step 3)

18. Execution result (Step 4)

19. Conclusion 1 This particular calculator can produce some built in graphs such as histogram, bar chart, pie chart, line chart, box-and-whisker plot, standard normal probability density function, linear regression line, quadratic regression line, log regression line, exponential regression line and power regression line.

20. Conclusion 2 Using List 4 in previous example, residual plots can be produced to check whether this data set is suitable for regression analysis or not.

21. Conclusion 3 Using basic statistics, the following tests besides the regression test can also be fulfilled: z test, one-sample t test, two-sample t test, paired t test, chi-square test for single variance and F test for two variances.

22. Conclusion 4 Using the built in permutation and combination functions, the probability mass function and cumulative mass function for the following discrete probability distributions can be found: binomial distribution, hyper- geometric distribution, geometric distribution, Poisson distribution and negative binomial distribution.

23. Conclusion 5 The built in list function can help doing many other analyses such as one way ANOVA, randomized block design, chi-square test for K ╳ 1 table, chi-square test for R ╳ C table, Wilcoxon rank sum test, etc. Generally speaking, this particular engineering calculator can accomplish lots of interesting statistical analyses if it’s fully utilized.

24. References CASIO fx-7400G PLUS manual. Berenson, Levine, & Krehbiel. Basic Business Statistics—Concepts and applications. Pearson International (Edition 11).

25. The End Thank you for your watching!